Scalable

Data

Aggregation

for

Dynamic

Events

in

Sensor

Networks

Computing

and

maintaining

network

structures

for

efficient

data

aggregation

incurs

high

overhead

for

dynamic

events

where

the

set

of

nodes

sensing

an

event

changes

with

time

Moreover

structured

approaches

are

sensitive

to

the

waiting-time

which

is

used

by

nodes

to

wait

for

packets

from

their

children

before

forwarding

the

packet

to

the

sink

Although

structure-less

approaches

can

address

these

issues

the

performance

does

not

scale

well

with

the

network

size

We

propose

a

semi-structured

approach

that

uses

a

structure-less

technique

locally

followed

by

Dynamic

Forwarding

on

an

implicitly

constructed

packet

forwarding

structure

to

support

network

scalability

The

structure

ToD

is

composed

of

multiple

shortest

path

trees

After

performing

local

aggregation

nodes

dynamically

decide

the

forwarding

tree

based

on

the

location

of

the

sources

The

key

principle

behind

ToD

is

that

adjacent

nodes

in

a

graph

will

have

low

stretch

in

one

of

these

trees

in

ToD

thus

resulting

in

early

aggregation

of

packets

Based

on

simulations

on

a

nodes

network

and

real

experiments

on

a

nodes

network

we

conclude

that

efficient

aggregation

in

large

scale

networks

can

be

achieved

by

our

semi-structured

approach

C.

-LSB-

Computer-Communication

Networks

-RSB-

Network

Architecture

and

Design

Wireless

communication

Design

Performance

This

work

was

partially

supported

by

NSF

's

CAREER

program

-LRB-

Grant

number

CNS

-RRB-

and

NSF

's

RI

program

-LRB-

Grant

number

CNS

-RRB-

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or

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provided

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are

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made

or

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and

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notice

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To

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SenSys

November

Boulder

Colorado

USA

Copyright

ACM

Data

aggregation

is

an

effective

technique

for

conserving

communication

energy

in

sensor

networks

In

sensor

networks

the

communication

cost

is

often

several

orders

of

magnitude

larger

than

the

computation

cost

Due

to

inherent

redundancy

in

raw

data

collected

from

sensors

in-network

data

aggregation

can

often

reduce

the

communication

cost

by

eliminating

redundancy

and

forwarding

only

the

extracted

information

from

the

raw

data

As

reducing

consumption

of

communication

energy

extends

the

network

lifetime

it

is

critical

for

sensor

networks

to

support

in-network

data

aggregation

Various

data

aggregation

approaches

have

been

proposed

for

data

gathering

applications

and

event-based

applications

These

approaches

make

use

of

cluster

based

structures

-LSB-

-RSB-

or

tree

based

structures

-LSB-

-RSB-

In

data

gathering

applications

such

as

environment

and

habitat

monitoring

-LSB-

-RSB-

nodes

periodically

report

the

sensed

data

to

the

sink

As

the

traffic

pattern

is

unchanging

these

structure-based

approaches

incur

low

maintenance

overhead

and

are

therefore

suitable

for

such

applications

However

in

event-based

applications

such

as

intrusion

detection

-LSB-

-RSB-

and

biological

hazard

detection

-LSB-

-RSB-

the

source

nodes

are

not

known

in

advance

Therefore

the

approaches

that

use

fixed

structures

can

not

efficiently

aggregate

data

while

the

approaches

that

change

the

structure

dynamically

incur

high

maintenance

overhead

-LSB-

-RSB-

The

goal

of

this

paper

is

to

design

a

scalable

and

efficient

data

aggregation

protocol

that

incurs

low

maintenance

overhead

and

is

suited

for

event-based

applications

Constructing

an

optimal

structure

for

data

aggregation

for

various

aggregation

functions

has

been

proven

to

be

an

NP-hard

problem

-LSB-

-RSB-

Although

heuristics

can

be

used

to

construct

structures

for

data

aggregation

another

problem

associated

with

the

convergecast

traffic

pattern

where

nodes

transmit

their

packets

to

the

cluster-head

or

parent

in

cluster

or

tree

structures

results

in

low

performance

of

structure

based

data

aggregation

protocols

In

-LSB-

-RSB-

the

simulation

results

show

that

the

packet

dropping

rate

in

Shortest

Path

Tree

-LRB-

SPT

-RRB-

is

higher

because

of

heavy

contention

caused

by

the

convergecast

traffic

This

results

in

more

packet

drops

and

increased

delays

As

a

result

enforcing

a

fixed

order

of

packet

transmissions

becomes

difficult

which

impacts

the

performance

of

data

aggregation

in

structured

approaches

Typically

packets

have

to

be

transmitted

in

a

fixed

order

from

leaves

to

the

root

in

a

tree-like

structure

to

achieve

maximum

aggregation

Dropped

packets

not

only

make

the

optimal

structure

sub-optimal

but

also

waste

energy

on

transmitting

packets

that

are

unable

to

reach

the

sink

In

-LSB-

-RSB-

it

shows

that

the

performance

gain

by

using

heuristics

to

create

the

Steiner

Minimum

Tree

-LRB-

SMT

-RRB-

for

aggregation

is

not

significant

compared

with

using

only

the

Shortest

Path

Tree

-LRB-

SPT

-RRB-

not

to

mention

that

the

overhead

of

constructing

such

a

structure

may

negate

the

benefit

resulting

from

data

aggregation

However

their

conclusions

were

based

on

the

assumption

of

randomly

located

data

sources

which

is

different

from

the

scenarios

in

event-based

sensor

networks

where

a

set

of

close-by

nodes

is

expected

to

sense

an

event

Realizing

the

shortcomings

of

structured

approaches

-LSB-

-RSB-

proposes

an

anycast

based

structure-less

approach

at

the

MAC

layer

to

aggregate

packet

It

involves

mechanisms

to

increase

the

chance

of

packets

meeting

at

the

same

node

-LRB-

Spatial

Aggregation

-RRB-

at

the

same

time

-LRB-

Temporal

Aggregation

-RRB-

As

the

approach

does

not

guarantee

aggregation

of

all

packets

from

a

single

event

the

cost

of

forwarding

unaggregated

packets

increases

with

the

scale

of

the

network

and

the

distance

of

the

event

from

the

sink

To

benefit

from

the

strengths

of

the

structured

and

the

structure-less

approaches

we

propose

a

semi-structured

approach

in

this

paper

The

main

challenge

in

designing

such

a

protocol

is

to

determine

the

packet

forwarding

strategy

in

absence

of

a

pre-constructed

global

structure

to

achieve

early

aggregation

Our

approach

uses

a

structure-less

technique

locally

followed

by

Dynamic

Forwarding

on

an

implicitly

constructed

packet

forwarding

structure

to

support

network

scalability

The

structure

ToD

-LRB-

Tree

on

Directed

acyclic

graph

-RRB-

is

composed

of

multiple

shortest

path

trees

After

performing

local

aggregation

nodes

dynamically

decide

the

forwarding

tree

based

on

the

location

of

the

source

nodes

The

key

principle

behind

ToD

is

that

adjacent

nodes

in

a

graph

will

have

low

stretch

in

at

least

one

of

these

trees

in

ToD

thus

resulting

in

early

aggregation

of

packets

This

paper

makes

the

following

contributions

We

propose

an

efficient

and

scalable

data

aggregation

mechanism

that

can

achieve

early

aggregation

without

incurring

any

overhead

of

constructing

a

structure

We

implement

the

ToD

approach

on

TinyOS

and

compare

its

performance

against

other

approaches

on

a

nodes

sensor

network

For

studying

the

scalability

aspects

of

our

approach

we

implement

ToD

in

the

simulator

and

study

its

performance

in

networks

of

up

to

nodes

The

organization

of

the

rest

of

the

paper

is

as

follows

Section

presents

background

and

related

work

Section

presents

the

structure-less

approach

Section

analyzes

the

performance

of

ToD

in

the

worst

case

The

performance

evaluation

of

the

protocols

using

simulations

and

experiments

is

presented

in

Section

Finally

Section

concludes

the

paper

Data

aggregation

has

been

an

active

research

area

in

sensor

networks

for

its

ability

to

reduce

energy

consumption

Some

works

focus

on

how

to

aggregate

data

from

different

nodes

-LSB-

-RSB-

some

focus

on

how

to

construct

and

maintain

a

structure

to

facilitate

data

aggregation

-LSB-

-RSB-

and

some

focus

on

how

to

efficiently

compress

and

aggregate

data

by

taking

the

correlation

of

data

into

consideration

-LSB-

-RSB-

As

our

work

focuses

on

how

to

facilitate

data

aggregation

without

incurring

the

overhead

of

constructing

a

structure

we

briefly

describe

the

structure-based

as

well

as

structure-less

approaches

in

current

research

In

-LSB-

-RSB-

the

authors

propose

the

LEACH

protocol

to

cluster

sensor

nodes

and

let

the

cluster-heads

aggregate

data

The

cluster-heads

then

communicate

directly

with

the

base

station

PEGASIS

-LSB-

-RSB-

extends

LEACH

by

organizing

all

nodes

in

a

chain

and

letting

nodes

be

the

head

in

turn

-LSB-

-RSB-

extend

PEGASIS

by

allowing

simultaneous

transmission

that

balances

the

energy

and

delay

cost

for

data

gathering

Both

LEACH

and

PEGASIS

assume

that

any

node

in

the

network

can

reach

the

base-station

directly

in

one-hop

which

limits

the

size

of

the

network

for

them

to

be

applicable

GIT

-LSB-

-RSB-

uses

a

different

approach

as

compared

to

LEACH

GIT

is

built

on

top

of

a

routing

protocol

Directed

Diffusion

-LSB-

-RSB-

which

is

one

of

the

earliest

proposed

attribute-based

routing

protocols

In

Directed

Diffusion

data

can

be

aggregated

opportunistically

when

they

meet

at

any

intermediate

node

Based

on

Directed

Diffusion

the

Greedy

Incremental

Tree

-LRB-

GIT

-RRB-

establishes

an

energy-efficient

tree

by

attaching

all

sources

greedily

onto

an

established

energy-efficient

path

and

pruning

less

energy

efficient

paths

However

due

to

the

overhead

of

pruning

branches

GIT

might

lead

to

high

cost

in

moving

event

scenarios

In

-LSB-

-RSB-

the

authors

propose

DCTC

Dynamic

Convoy

Tree-Based

Collaboration

to

reduce

the

overhead

of

tree

migration

in

mobile

event

scenarios

DCTC

assumes

that

the

distance

to

the

event

is

known

to

each

sensor

and

uses

the

node

near

the

center

of

the

event

as

the

root

to

construct

and

maintain

the

aggregation

tree

dynamically

However

it

involves

heavy

message

exchanges

which

might

offset

the

benefit

of

aggregation

in

large-scale

networks

From

the

simulation

results

in

DCTC

-LSB-

-RSB-

the

energy

consumption

of

tree

expansion

pruning

and

reconfiguration

is

about

of

the

data

collection

In

-LSB-

-RSB-

the

authors

propose

an

aggregation

tree

construction

algorithm

to

simultaneously

approximate

the

optimum

trees

for

all

non-decreasing

and

concave

aggregation

functions

The

algorithm

uses

a

simple

min-cost

perfect

matching

to

construct

the

tree

-LSB-

-RSB-

also

uses

similar

min-cost

matching

process

to

construct

an

aggregation

tree

that

takes

the

data

fusion

cost

into

consideration

Other

works

such

as

SMT

-LRB-

Steiner

Minimum

Tree

-RRB-

and

MST

-LRB-

Multiple

Shared

Tree

-RRB-

for

multicast

algorithms

which

can

be

used

in

data

aggregation

-LSB-

-RSB-

build

a

structure

in

advance

for

data

aggregation

In

addition

to

their

complexity

and

overhead

they

are

only

suitable

for

networks

where

the

sources

are

known

in

advance

Therefore

they

are

not

suitable

for

networks

with

mobile

events

Moreover

fixed

tree

structure

might

have

long

stretch

between

adjacent

nodes

A

stretch

of

two

nodes

u

and

v

in

a

tree

T

on

a

graph

G

is

the

ratio

between

the

distance

from

node

u

to

v

in

T

and

their

distance

in

G.

Long

stretch

implies

packets

from

adjacent

nodes

have

to

be

forwarded

many

hops

away

before

they

can

be

aggregated

This

problem

has

been

studied

as

MSST

-LRB-

Minimum

Stretch

Spanning

Tree

-RRB-

-LSB-

-RSB-

and

MAST

-LRB-

Minimum

Average

Stretch

Spanning

Tree

-RRB-

-LSB-

-RSB-

They

are

also

NP-hard

problems

and

it

has

been

shown

that

for

any

graph

the

lower

bound

of

the

average

stretch

is

O

-LRB-

log

-LRB-

n

-RRB-

-RRB-

-LSB-

-RSB-

and

it

can

be

as

high

as

O

-LRB-

n

-RRB-

for

the

worst

case

-LSB-

-RSB-

Even

for

a

grid

network

it

has

been

shown

that

the

lower

bound

for

the

worst

case

is

O

-LRB-

n

-RRB-

-LSB-

-RSB-

-LSB-

-RSB-

proposes

a

polynomial

time

algorithm

to

construct

a

group-independent

spanning

tree

that

can

achieve

O

-LRB-

log

-LRB-

n

-RRB-

-RRB-

stretch

However

the

delay

in

-LSB-

-RSB-

is

high

in

large

networks

if

only

nodes

near

the

sink

are

triggered

-LSB-

-RSB-

is

the

first

proposed

structure-less

data

aggregation

protocol

that

can

achieve

high

aggregation

without

incurring

the

overhead

of

structure

approaches

-LSB-

-RSB-

uses

anycast

to

forward

packets

to

one-hop

neighbors

that

have

packets

for

aggregation

It

can

efficiently

aggregate

packets

near

the

sources

and

effectively

reduce

the

number

of

transmissions

However

it

does

not

guarantee

the

aggregation

of

all

packets

from

a

single

event

As

the

network

grows

the

cost

of

forwarding

packets

that

were

unable

to

be

aggregated

will

negate

the

benefit

of

energy

saving

resulted

from

eliminating

the

control

overhead

In

order

to

get

benefit

from

structure-less

approaches

even

in

large

networks

scalability

has

to

be

considered

in

the

design

of

the

aggregation

protocol

In

this

paper

we

propose

a

scalable

structure-less

protocol

ToD

that

can

achieve

efficient

aggregation

even

in

large

networks

ToD

uses

a

semi-structure

approach

that

does

not

have

the

long

stretch

problem

in

fixed

structure

nor

incur

structure

maintenance

overhead

of

dynamic

structure

and

further

improves

the

performance

of

the

structure-less

approach

As

described

before

the

goal

of

our

protocol

is

to

achieve

aggregation

of

data

near

the

sources

without

explicitly

constructing

a

structure

for

mobile

event

scenarios

Aggregating

packets

near

the

sources

is

critical

for

reducing

the

number

of

transmissions

Aggregating

without

using

an

explicit

structure

reduces

the

overhead

of

construction

and

maintenance

of

the

structure

In

this

section

we

propose

a

highly

scalable

approach

that

is

suitable

for

very

large

sensor

networks

Our

protocol

is

based

on

the

Data

Aware

Anycast

-LRB-

DAA

-RRB-

and

Randomized

Waiting

-LRB-

RW

-RRB-

approaches

proposed

in

-LSB-

-RSB-

There

are

two

phases

in

our

protocol

DAA

and

Dynamic

Forwarding

In

the

first

phase

packets

are

forwarded

and

aggregated

to

a

selected

node

termed

aggregator

using

DAA

In

DAA

-LSB-

-RSB-

packets

were

destined

to

the

sink

whereas

in

our

approach

they

are

destined

to

an

aggregator

In

the

second

phase

the

leftover

un-aggregated

or

partially

aggregated

packets

are

forwarded

on

a

structure

termed

Tree

on

DAG

-LRB-

ToD

-RRB-

for

further

aggregation

First

we

briefly

describe

the

DAA

protocol

proposed

in

-LSB-

-RSB-

Data

Aware

Anycast

-LSB-

-RSB-

Data

Aware

Anycast

is

a

structure-less

protocol

that

aggregates

packets

by

improving

the

Spatial

and

Temporal

In

rest

of

this

paper

we

use

DAA

or

Data

Aware

Anycast

to

refer

to

the

combination

of

the

two

approaches

vergence

Spatial

convergence

and

temporal

convergence

during

transmission

are

two

necessary

conditions

for

aggregation

Packets

have

to

be

transmitted

to

the

same

node

at

the

same

time

to

be

aggregated

Structured

approaches

achieve

these

two

conditions

by

letting

nodes

transmit

packets

to

their

parents

in

the

aggregation

tree

and

parents

wait

for

packets

from

all

their

children

before

transmitting

the

aggregated

packets

Without

explicit

message

exchanges

in

structure-less

aggregation

nodes

do

not

know

where

they

should

send

packets

to

and

how

long

they

should

wait

for

aggregation

Therefore

improving

spatial

or

temporal

convergence

is

critical

for

improving

the

chance

of

aggregation

Spatial

Convergence

is

achieved

by

using

anycast

to

forward

packets

to

nodes

that

can

achieve

aggregation

Anycast

is

a

routing

scheme

whereby

packets

are

forwarded

to

the

best

one

or

any

one

of

a

group

of

target

destinations

based

on

some

routing

metrics

By

exploiting

the

nature

of

wireless

radio

transmission

in

sensor

networks

where

all

nodes

within

the

transmission

range

can

receive

the

packet

nodes

are

able

to

tell

if

they

can

aggregate

the

transmitting

packet

and

the

anycast

mechanism

allows

the

sender

to

forward

packets

to

any

one

of

them

Transmitting

packets

to

nodes

that

can

achieve

aggregation

reduces

the

number

of

remaining

packets

in

the

network

thereby

reducing

the

total

number

of

transmissions

Temporal

Convergence

is

used

to

further

improve

the

aggregation

Randomized

Waiting

is

a

simple

technique

for

achieving

temporal

convergence

in

which

nodes

wait

for

a

random

delay

before

transmitting

In

mobile

event

triggered

networks

nodes

are

unable

to

know

which

nodes

are

triggered

and

have

packets

to

transmit

in

advance

Therefore

nodes

can

not

know

if

they

should

wait

for

their

upstream

nodes

and

how

long

they

should

wait

for

aggregation

A

naive

approach

of

using

a

fixed

delay

depending

on

the

distance

to

the

sink

may

make

the

detection

delay

very

high

For

example

as

shown

in

Fig.

nodes

closer

to

the

sink

must

wait

longer

for

packets

from

possible

upstream

nodes

if

fixed

waiting

time

is

employed

When

events

are

closer

to

the

sink

the

longer

delay

chosen

by

nodes

closer

to

the

sink

is

unnecessary

Random

delay

is

used

to

avoid

long

delay

in

large

networks

while

increasing

the

chance

of

aggregation

sink

n

nodes

triggered

by

an

event

Figure

Longer

delay

is

unnecessary

but

is

inevitable

using

fixed

delay

when

the

event

is

closer

to

the

sink

Nodes

closer

to

the

sink

have

longer

delay

-LRB-

-RRB-

because

they

have

to

wait

for

packets

from

possible

upstream

nodes

When

a

node

detects

an

event

and

generates

a

packet

for

reporting

it

picks

a

random

delay

between

and

before

transmitting

where

is

a

network

parameter

that

specifies

the

maximum

delay

After

delaying

the

packet

the

node

broadcasts

an

RTS

packet

containing

an

Aggregation

ID

In

-LSB-

-RSB-

the

timestamp

is

used

as

the

Aggregation

ID

which

means

that

packets

generated

at

the

same

time

can

be

aggregated

When

a

node

receives

an

RTS

packet

it

checks

if

it

has

packets

with

the

same

Aggregation

ID

If

it

does

it

has

higher

priority

for

replying

with

a

CTS

than

nodes

that

do

not

have

packets

for

aggregation

The

priority

is

decided

by

the

delay

of

replying

a

CTS

packet

Nodes

with

higher

priority

reply

a

CTS

with

shorter

delay

If

a

node

overhears

any

traffic

before

transmitting

its

CTS

packet

it

cancels

the

CTS

transmission

in

order

to

avoid

collision

of

multiple

CTS

responses

at

the

sender

Therefore

nodes

can

send

their

packets

for

aggregation

as

long

as

at

least

one

of

its

neighbors

has

a

packet

with

the

same

Aggregation

ID

More

details

and

extensions

of

the

DAA

approach

can

be

found

in

-LSB-

-RSB-

However

DAA

can

not

guarantee

that

all

packets

will

be

aggregated

into

one

packet

When

more

packets

are

transmitted

from

sources

to

the

sink

without

aggregation

more

energy

is

wasted

This

effect

becomes

more

severe

when

the

network

is

very

large

and

the

sources

are

very

far

away

from

the

sink

Therefore

instead

of

forwarding

packets

directly

to

the

sink

when

DAA

can

not

aggregate

packets

any

more

we

propose

the

use

of

Dynamic

Forwarding

for

further

packet

aggregation

We

now

describe

the

Dynamic

Forwarding

and

the

construction

of

ToD

Dynamic

Forwarding

over

ToD

sink

nodes

triggered

by

event

B

nodes

triggered

by

event

A

Figure

Fixed

tree

structure

for

aggregation

can

have

long

distance

-LRB-

link-stretch

-RRB-

between

adjacent

nodes

as

in

the

case

of

nodes

triggered

by

event

B

In

this

example

we

assume

that

nodes

in

the

range

of

event

B

are

within

transmission

range

of

each

other

We

adopt

the

pre-constructed

structure

approach

in

the

second

phase

to

achieve

further

aggregation

Having

a

structure

to

direct

all

packets

to

a

single

node

is

inevitable

if

we

want

to

aggregate

all

packets

into

one

Constructing

a

structure

dynamically

with

explicit

message

exchanges

incurs

high

overhead

Therefore

we

use

an

implicitly

computed

pre-constructed

structure

that

remains

unchanged

for

relatively

long

time

periods

-LRB-

several

hours

or

days

-RRB-

However

using

a

fixed

structure

has

the

long

stretch

problem

as

described

in

Section

Take

Fig.

as

an

example

of

pre-computed

tree

structure

where

gray

nodes

are

the

sources

The

fixed

tree

structure

works

well

if

the

nodes

that

generate

packets

are

triggered

by

event

A

because

their

packets

can

be

aggregated

immediately

on

the

tree

However

if

the

nodes

that

generate

packets

are

triggered

by

event

B

their

packets

can

not

be

aggregated

even

if

they

are

adjacent

to

each

other

Therefore

we

design

a

dynamic

forwarding

mechanism

over

ToD

to

avoid

the

problem

of

long

stretch

ToD

in

One

Dimensional

Networks

network

one

row

instance

of

the

network

sink

Figure

We

illustrate

the

ToD

construction

from

one

row

's

point

of

view

to

simplify

the

discussion

For

illustrating

the

concept

of

ToD

we

first

describe

the

construction

of

ToD

for

a

-LRB-

a

single

row

of

nodes

-RRB-

network

as

shown

in

Fig.

We

assume

that

the

nodes

can

communicate

with

their

adjacent

nodes

in

the

same

row

through

one

hop

We

define

a

cell

as

a

square

with

side

length

where

is

greater

than

the

maximum

diameter

of

the

area

that

an

event

can

span

The

network

is

divided

into

cells

These

cells

are

grouped

into

clusters

called

F-clusters

-LRB-

First-level

clusters

-RRB-

The

size

of

the

F-clusters

must

be

large

enough

to

cover

the

cells

an

event

can

span

which

is

two

when

we

only

consider

cells

in

the

network

All

nodes

in

F-clusters

send

their

packets

to

their

cluster-heads

called

F-aggregators

-LRB-

First-level

aggregators

-RRB-

Note

that

nodes

in

the

F-cluster

can

be

multiple

hops

away

from

the

F-aggregator

The

formation

of

the

clusters

and

the

election

of

the

aggregators

are

discussed

later

in

Section

Each

F-aggregator

then

creates

a

shortest

path

to

the

sink

Therefore

the

structure

is

a

shortest

path

tree

where

the

root

is

the

sink

and

the

leaves

are

F-aggregators

We

call

this

tree

an

F-Tree

Fig.

-LRB-

a

-RRB-

shows

the

construction

of

the

F-Tree

In

addition

to

the

F-clusters

we

create

the

second

type

of

clusters

S-clusters

-LRB-

Second-level

clusters

-RRB-

for

these

cells

The

size

of

an

S-cluster

must

also

be

large

enough

to

cover

all

cells

spanned

by

an

event

and

it

must

interleave

with

the

F-clusters

so

it

can

cover

adjacent

cells

in

different

F-clusters

Each

S-cluster

also

has

a

cluster-head

S-aggregator

for

aggregating

packets

Each

S-aggregator

creates

a

shortest

path

to

the

sink

and

forms

a

second

shortest

path

tree

in

the

network

We

call

it

S-Tree

The

illustration

of

an

S-Tree

is

shown

in

Fig.

-LRB-

b

-RRB-

For

all

sets

of

nearby

cells

that

can

be

triggered

by

an

event

either

they

will

be

in

the

same

F-cluster

or

they

will

be

in

the

same

S-cluster

This

property

is

exploited

by

Dynamic

Forwarding

to

avoid

the

long

stretch

problem

discussed

earlier

After

the

S-Tree

is

constructed

the

F-aggregators

connect

themselves

to

the

S-aggregators

of

S-clusters

which

its

F-cluster

overlaps

with

as

shown

in

Fig.

-LRB-

c

-RRB-

For

example

in

Fig.

-LRB-

c

-RRB-

the

F-aggregator

connects

to

S-aggregators

and

because

its

F-cluster

overlaps

with

S-cluster

and

Thus

the

combination

of

F-Tree

and

S-Tree

creates

a

A

B

C

D

Cells

Other

nodes

in

the

network

F-Aggregators

Cells

with

packets

F-Tree

S-Tree

Overlapping

ToD

-LRB-

a

-RRB-

-LRB-

b

-RRB-

-LRB-

c

-RRB-

A

B

C

D

F-clusters

A

B

C

D

S-clusters

S-Aggregators

Figure

The

construction

of

F-Tree

S-Tree

and

ToD

-LRB-

a

-RRB-

Leaf

nodes

are

cells

Pairs

of

neighbor

cells

define

F-clusters

Each

F-cluster

has

an

F-aggregator

and

F-aggregators

form

the

F-Tree

-LRB-

b

-RRB-

Each

pair

of

adjacent

cells

not

in

the

same

F-cluster

form

an

S-cluster

Each

S-cluster

has

an

S-aggregator

and

S-aggregators

form

the

S-Tree

Nodes

on

the

network

boundary

do

not

need

to

be

in

any

S-cluster

-LRB-

c

-RRB-

Each

F-aggregator

connects

to

two

S-aggregators

of

S-clusters

which

its

F-cluster

overlaps

with

This

structure

called

the

Tree

on

DAG

or

ToD

F-aggregator

in

ToD

uses

Dynamic

Forwarding

to

forward

packets

to

the

root

or

through

an

S-aggregator

in

the

S-Tree

based

on

where

the

packets

come

from

rected

Acyclic

Graph

which

we

refer

to

as

the

ToD

-LRB-

Tree

on

DAG

-RRB-

Nodes

first

use

the

Data

Aware

Anycast

-LRB-

DAA

-RRB-

approach

to

aggregate

as

many

packets

as

possible

When

no

further

aggregation

can

be

achieved

by

DAA

nodes

forward

their

packets

to

the

F-aggregator

in

its

F-cluster

If

an

event

only

triggers

nodes

within

a

single

F-cluster

its

packets

can

be

aggregated

at

the

F-aggregator

and

be

forwarded

to

the

sink

using

the

F-Tree

However

in

case

the

event

spans

multiple

F-clusters

the

corresponding

packets

will

be

forwarded

to

different

F-aggregators

As

we

assumed

that

the

event

size

is

not

larger

than

the

size

of

a

cell

an

event

on

the

boundary

of

F-clusters

will

only

trigger

nodes

in

cells

on

the

boundary

of

the

F-clusters

By

the

construction

of

S-clusters

adjacent

cells

on

the

boundary

of

F-clusters

belong

to

the

same

S-cluster

Thus

F-aggregators

can

exploit

the

information

collected

from

received

packets

to

select

the

S-aggregator

that

is

best

suited

for

further

aggregation

This

information

is

obtained

from

the

source

of

traffic

that

can

be

encoded

in

the

packets

Often

such

information

is

readily

available

in

the

packet

Otherwise

extra

bits

can

be

used

to

indicate

which

cell

the

packet

comes

from

Consider

the

example

in

Fig.

-LRB-

c

-RRB-

Since

the

maximum

number

of

cells

an

event

can

span

is

two

either

these

two

cells

are

in

the

same

F-cluster

or

they

are

in

the

same

S-cluster

If

they

are

in

the

same

F-cluster

their

packets

can

be

aggregated

at

the

F-aggregator

For

example

if

the

event

spans

A

and

B

knows

that

no

other

F-cluster

has

packets

for

aggregation

and

it

can

forward

the

packets

using

the

F-Tree

If

the

event

spans

two

cells

that

are

in

different

F-clusters

the

two

F-aggregators

in

the

two

F-clusters

will

receive

packets

only

from

one

of

their

cells

The

F-aggregators

then

conjecture

which

F-cluster

might

also

have

packets

based

on

which

cells

the

packets

come

from

For

example

if

the

event

spans

C

and

D

will

only

receive

packets

from

C.

Therefore

can

know

either

the

event

happens

only

in

C

or

the

event

spans

C

and

D.

Consequently

can

forward

packets

to

the

S-aggregator

of

its

overlapped

S-clusters

covering

C.

Also

will

forward

its

packets

to

if

packets

only

come

from

D.

Therefore

these

packets

can

be

aggregated

at

Note

that

we

do

not

specifically

assign

cells

on

the

boundary

of

the

network

to

any

S-cluster

They

do

not

need

to

be

in

any

S-cluster

if

they

are

not

adjacent

to

any

other

F-cluster

or

they

can

be

assigned

to

the

same

S-cluster

as

its

adjacent

cell

The

ToD

for

the

one

dimensional

network

has

the

following

property

Property

For

any

two

adjacent

nodes

in

ToD

in

one

dimensional

network

their

packets

will

be

aggregated

either

at

a

first

level

aggregator

or

will

be

aggregated

at

a

second

level

aggregator

Proof

There

are

only

three

possibilities

when

an

event

triggers

nodes

to

generate

packets

If

only

nodes

in

one

cell

are

triggered

and

generate

the

packets

their

packets

can

be

aggregated

at

one

F-aggregator

since

all

nodes

in

a

cell

reside

in

the

same

F-cluster

and

all

packets

in

an

F-cluster

will

be

aggregated

at

the

F-aggregator

If

an

event

triggers

nodes

in

two

cells

and

these

two

cells

are

in

the

same

F-cluster

the

packets

can

be

aggregated

at

the

F-aggregator

as

well

If

an

event

triggers

nodes

in

two

cells

but

these

two

cells

are

in

different

F-clusters

they

must

reside

in

the

same

S-cluster

because

S-clusters

and

F-clusters

are

interleaved

Moreover

packets

in

one

F-cluster

will

only

originate

from

the

cell

that

is

closer

to

the

other

F-cluster

that

also

has

packets

Therefore

the

F-aggregator

can

forward

packets

to

the

S-aggregator

for

aggregation

accordingly

and

packets

will

be

aggregated

at

the

S-aggregator

Since

the

cell

is

not

smaller

than

the

maximum

size

of

an

event

it

is

impossible

for

an

event

to

trigger

more

than

two

cells

and

this

completes

the

proof

ToD

in

Two

Dimensional

Networks

Section

only

demonstrates

the

construction

for

one

row

of

nodes

to

illustrate

the

basic

idea

of

dynamic

forwarding

and

it

works

because

each

cell

is

only

adjacent

to

one

-LRB-

or

if

the

cell

is

on

the

boundary

of

the

network

-RRB-

of

the

F-clusters

Therefore

if

an

event

spans

two

cells

the

two

cells

are

either

in

the

same

F-cluster

or

in

the

same

S-cluster

and

the

F-aggregator

can

conjecture

whether

to

forward

the

packets

to

the

S-aggregator

or

to

the

sink

directly

When

we

consider

other

cells

and

F-clusters

in

the

adjacent

row

a

cell

on

the

boundary

of

an

F-cluster

might

be

adjacent

to

multiple

F-clusters

If

an

event

spans

multiple

cells

each

F-aggregator

may

have

multiple

choices

of

S-aggregators

if

the

cells

in

their

F-cluster

are

adjacent

to

multiple

F-clusters

If

these

F-aggregators

select

different

S-aggregators

their

packets

will

not

be

aggregated

However

the

ideas

presented

in

networks

can

be

extended

for

the

networks

But

instead

of

guaranteeing

that

packets

will

be

aggregated

within

two

steps

as

in

the

case

-LRB-

aggregating

either

at

an

F-aggregator

or

an

S-aggregator

-RRB-

the

ToD

in

guarantees

that

the

packets

can

be

aggregated

within

three

steps

We

first

define

the

cells

and

clusters

in

two

dimensions

For

the

ease

of

understanding

we

use

grid

clustering

to

illustrate

the

construction

As

defined

before

the

size

of

a

cell

is

not

less

than

the

maximum

size

of

an

event

and

an

F-cluster

must

cover

all

the

cells

that

an

event

might

span

which

is

four

cells

in

grid-clustering

Therefore

the

entire

network

is

divided

into

F-clusters

and

each

F-cluster

contains

four

cells

The

S-clusters

have

to

cover

all

adjacent

cells

in

different

F-clusters

Each

F-cluster

and

S-cluster

also

has

a

cluster-head

acting

as

the

aggregator

to

aggregate

packets

Fig.

shows

a

network

with

its

F-clusters

and

S-clusters

Since

the

size

of

a

cell

-LRB-

one

side

of

the

square

cell

-RRB-

must

be

greater

or

equal

to

the

maximum

size

of

an

event

-LRB-

diameter

of

the

event

-RRB-

an

event

can

span

only

one

two

three

or

four

cells

as

illustrated

in

Fig.

If

the

event

only

spans

cells

in

the

same

F-cluster

the

packets

can

be

aggregated

at

the

F-aggregator

Therefore

we

only

consider

scenarios

where

an

event

spans

cells

in

multiple

F-clusters

-LRB-

a

-RRB-

F-clusters

-LRB-

c

-RRB-

S-cluters

A

B

C

D

-LRB-

b

-RRB-

Cells

G

H

I

E

F

Figure

Grid-clustering

for

a

two-dimension

network

-LRB-

a

-RRB-

The

network

is

divided

into

F-clusters

-LRB-

b

-RRB-

Each

F-cluster

contains

four

cells

For

example

the

F-cluster

A

in

-LRB-

a

-RRB-

contains

cell

and

-LRB-

c

-RRB-

The

S-clusters

have

to

cover

all

adjacent

cells

in

different

F-clusters

Each

S-cluster

contains

four

cells

from

four

different

F-clusters

Figure

The

possible

numbers

of

cells

an

event

may

span

in

cells

which

are

one

two

three

and

four

from

left

to

right

The

four

cells

in

each

case

are

any

instance

of

four

cells

in

the

network

They

may

be

in

the

same

F-cluster

or

different

F-clusters

Fig.

shows

four

basic

scenarios

that

an

F-aggregator

may

encounter

when

collecting

all

packets

generated

in

its

F-cluster

All

other

scenarios

are

only

different

combinations

of

these

four

scenarios

If

packets

originate

from

three

or

four

cells

in

the

same

F-cluster

the

F-aggregator

knows

that

no

other

nodes

in

other

F-clusters

have

packets

and

it

can

forward

the

packets

directly

to

the

sink

If

only

one

or

two

cells

generate

packets

it

is

possible

that

other

F-clusters

also

have

packets

We

assume

that

the

region

spanned

by

an

event

is

contiguous

So

simultaneous

occurrence

of

scenarios

of

-LRB-

a

-RRB-

and

-LRB-

c

-RRB-

or

-LRB-

b

-RRB-

and

-LRB-

d

-RRB-

is

impossible

in

the

F-cluster

However

such

scenarios

are

possible

in

presence

of

losses

in

a

real

environment

where

packets

from

third

or

fourth

cluster

are

lost

In

such

cases

the

F-aggregator

can

just

forward

the

packets

directly

to

the

sink

because

no

other

F-cluster

will

have

packets

from

the

same

event

Figure

All

possible

scenarios

in

an

F-aggregator

's

point

of

view

Each

case

shows

F-clusters

and

the

aggregator

of

the

center

F-cluster

is

making

the

decision

The

dark

grayed

squares

are

cells

that

generate

packets

and

the

light

grayed

squares

represent

the

corresponding

S-cluster

of

the

dark

grayed

cells

When

the

F-aggregator

collects

all

packets

within

its

cluster

it

knows

which

cells

the

packets

come

from

and

forwards

the

packets

to

best

suited

S-aggregator

for

further

aggregation

For

example

if

the

packets

only

come

from

one

cell

as

in

case

-LRB-

a

-RRB-

in

Fig.

the

F-aggregator

can

forward

the

packet

to

the

S-aggregator

of

the

S-cluster

that

covers

that

cell

However

if

packets

come

from

two

cells

in

an

F-cluster

the

two

cells

must

be

in

different

S-clusters

For

example

as

in

Fig.

where

the

F-aggregator

of

F-cluster

X

receives

packets

from

two

cells

is

the

combination

of

case

-LRB-

a

-RRB-

and

-LRB-

b

-RRB-

in

Fig.

It

is

possible

that

the

F-aggregator

of

F-cluster

Y

may

receive

packets

from

cells

as

in

Fig.

-LRB-

c

-RRB-

-LRB-

d

-RRB-

or

both

Since

the

F-aggregator

of

F-cluster

X

does

not

know

which

case

the

F-aggregator

of

F-cluster

Y

encounters

it

does

not

know

which

S-aggregator

to

forward

packets

to

To

guarantee

the

aggregation

the

F-aggregator

of

F-cluster

X

forwards

the

packet

through

two

S-aggregators

that

covers

cell

and

therefore

packets

can

meet

at

least

at

one

S-aggregator

If

both

F-aggregators

receive

packets

from

two

cells

in

its

cluster

to

guarantee

that

the

packets

can

meet

at

least

at

one

S-aggregator

these

two

F-aggregators

must

select

the

S-aggregator

deterministically

The

strategy

is

to

select

the

S-aggregator

that

is

closer

to

the

sink

If

the

packets

meet

at

the

first

S-aggregator

it

does

not

need

to

forward

packets

to

the

second

S-aggregator

The

S-aggregator

only

forwards

packets

to

the

second

S-aggregator

if

the

packets

it

received

only

come

from

two

cells

in

one

F-cluster

We

will

present

a

simplified

construction

later

-LRB-

in

Section

-RRB-

for

the

selection

of

S-aggregators

F-cluster

X

F-cluster

Y

S-cluster

I

S-cluster

II

Figure

The

F-aggregators

have

two

choices

for

S-aggregators

if

they

receive

packets

from

two

cells

To

guarantee

that

the

packets

can

meet

at

least

at

one

S-aggregator

the

second

S-aggregator

must

wait

longer

than

the

first

S-aggregator

Therefore

if

the

S-aggregator

receives

packets

from

only

one

cell

it

waits

longer

to

wait

for

possible

packets

forwarded

by

the

other

S-aggregator

because

it

could

be

the

second

S-aggregator

of

the

other

F-aggregator

Fig.

shows

an

example

of

one

F-aggregator

sending

packets

to

the

first

S-aggregator

and

then

the

second

S-aggregator

while

the

other

F-aggregator

sends

packets

directly

to

the

second

S-aggregator

As

long

as

the

second

S-aggregator

waits

suf-ficiently

longer

than

the

first

S-aggregator

the

packets

can

be

aggregated

at

the

second

S-aggregator

F-aggregators

st

S-aggregators

nd

S-aggregators

Figure

Depending

on

how

many

cells

generate

packets

in

its

F-cluster

one

F-aggregator

sends

packets

to

two

S-aggregators

while

the

other

F-aggregator

sends

packets

to

only

one

S-aggregator

We

assume

that

the

sink

is

located

at

bottom-left

of

the

network

The

ToD

for

the

two

dimension

networks

has

the

following

property

Property

For

any

two

adjacent

nodes

in

ToD

their

packets

will

be

aggregated

at

the

F-aggregator

at

the

st

S-aggregator

or

at

the

nd

S-aggregator

Proof

First

we

define

the

F-aggregator

X

as

the

aggregator

of

F-cluster

X

and

S-aggregator

I

as

the

aggregator

of

S-cluster

I

and

so

forth

For

packets

generated

only

in

one

F-cluster

their

packets

can

be

aggregated

at

the

F-aggregator

since

all

packets

in

the

F-cluster

will

be

sent

to

the

F-aggregator

If

an

event

triggers

nodes

in

different

F-clusters

there

are

only

three

cases

First

only

one

cell

in

each

F-cluster

generates

packets

In

this

case

all

cells

having

packets

will

be

in

the

same

S-cluster

since

the

adjacent

cells

in

different

F-clusters

are

all

in

the

same

S-cluster

Therefore

their

packets

can

be

aggregated

at

the

S-aggregator

Second

the

event

spans

three

cells

and

and

two

of

them

are

in

one

F-cluster

and

one

of

them

is

in

the

other

F-cluster

Without

loss

of

generality

we

assume

that

and

are

in

the

same

F-cluster

F-cluster

X

and

is

in

the

other

F-cluster

F-cluster

Y

Moreover

must

be

adjacent

to

either

or

and

let

us

assume

that

it

is

From

the

ToD

construction

we

know

that

and

will

be

in

the

same

S-cluster

S-cluster

II

and

will

be

in

another

S-cluster

S-cluster

I.

Fig.

illustrates

one

instance

of

this

case

First

the

F-aggregator

X

will

aggregate

packets

from

and

because

they

are

in

the

same

F-cluster

and

forward

the

aggregated

packets

through

S-aggregator

I

to

S-aggregator

II

or

the

other

way

around

because

is

in

S-cluster

I

and

is

in

S-cluster

II

F-aggregator

Y

will

aggregate

packets

from

and

forward

packets

to

S-aggregator

II

because

is

in

S-cluster

II

Because

packets

of

F-aggregator

Y

only

come

from

they

will

have

longer

delay

in

S-aggregator

II

in

order

to

wait

for

packets

being

forwarded

through

the

other

S-aggregator

In

the

mean

time

if

F-aggregator

X

forwards

packets

to

S-aggregator

II

first

the

packets

can

be

aggregated

at

S-aggregator

II

If

F-aggregator

X

forwards

packets

to

S-aggregator

I

first

S-aggregator

I

will

forward

packets

to

S-aggregator

II

with

shorter

delay

because

the

packets

come

from

two

cells

in

one

F-cluster

therefore

their

packets

can

also

be

aggregated

at

S-aggregator

II

In

the

third

case

the

event

spans

four

cells

Two

of

them

will

be

in

one

F-cluster

and

the

other

two

will

be

in

the

other

F-cluster

Without

loss

of

generality

we

can

assume

that

cells

and

are

in

F-cluster

X

and

cells

and

are

in

F-cluster

Y

and

and

are

adjacent

and

are

adjacent

From

the

ToD

construction

and

will

be

in

one

S-cluster

S-cluster

I

and

and

will

be

in

the

other

S-cluster

S-cluster

II

Because

from

S-aggregator

I

and

II

F-aggregator

X

and

Y

choose

one

that

is

closer

to

the

sink

as

the

first

S-aggregator

they

will

choose

the

same

S-aggregator

Therefore

their

packets

can

be

aggregated

at

the

first

S-aggregator

and

this

completes

the

proof

Though

in

this

section

we

assume

that

the

size

of

an

event

is

smaller

than

the

size

of

the

cell

our

approach

can

still

work

correctly

and

perform

more

efficiently

than

DAA

even

if

the

size

of

the

event

is

not

known

in

advance

This

is

because

the

nodes

will

use

Dynamic

Forwarding

over

ToD

only

at

second

phase

where

the

aggregation

by

DAA

is

no

longer

achievable

Therefore

at

worst

our

approach

just

falls

back

to

DAA

Section

shows

that

in

experiments

ToD

improves

the

performance

of

DAA

by

even

if

the

size

of

the

event

is

greater

than

the

size

of

a

cell

Clustering

and

Aggregator

Selection

In

this

paper

we

use

grid-clustering

to

construct

the

cells

and

clusters

Although

other

clustering

methods

such

as

clustering

based

on

hexagonal

or

triangular

tessellation

can

also

be

used

we

do

not

explore

them

further

in

this

paper

In

principle

any

clustering

would

work

as

long

as

they

satisfy

the

following

conditions

First

the

size

of

the

cell

must

be

greater

than

or

equal

to

the

maximum

size

of

an

event

Second

the

F-cluster

and

S-cluster

must

cover

the

cells

that

an

event

may

span

and

the

S-cluster

must

cover

the

adjacent

cells

in

different

F-clusters

As

opposed

to

defining

an

arbitrary

clustering

using

grid-clustering

has

two

advantages

First

the

size

of

the

grid

can

be

easily

determined

by

configuring

the

grid

size

as

a

network

parameter

Second

as

long

as

the

geographic

location

is

known

to

the

node

the

cell

F-cluster

and

S-cluster

it

belongs

to

can

be

determined

immediately

without

any

communication

Geographic

information

is

essential

in

sensor

networks

therefore

we

assume

that

sensor

nodes

know

their

physical

location

by

configuration

at

deployment

a

GPS

device

or

localization

protocols

-LSB-

-RSB-

As

a

consequence

all

the

cells

F-clusters

and

S-clusters

can

be

implicitly

constructed

After

the

grids

are

constructed

nodes

in

an

F-cluster

and

S-cluster

have

to

select

an

aggregator

for

their

cluster

Because

the

node

that

acts

as

the

aggregator

consumes

more

energy

than

other

nodes

nodes

should

play

the

role

of

aggregator

in

turn

in

order

to

evenly

distribute

the

energy

consumption

among

all

nodes

Therefore

the

aggregator

selection

process

must

be

performed

periodically

However

the

frequency

of

updating

the

aggregator

can

be

very

low

from

once

in

several

hours

to

once

in

several

days

depending

on

the

capacity

of

the

battery

on

the

nodes

Nodes

can

elect

themselves

as

the

cluster-head

with

probability

based

on

metrics

such

as

the

residual

energy

and

advertise

to

all

nodes

in

its

cluster

In

case

two

nodes

select

themselves

as

the

cluster-head

the

node-id

can

be

used

to

break

the

tie

The

other

approach

is

that

the

nodes

in

a

cluster

use

a

hash

function

to

hash

the

current

time

to

a

node

within

that

cluster

and

use

that

node

as

the

aggregator

Nodes

have

to

know

the

address

of

all

nodes

in

its

F-cluster

and

sort

them

by

their

node

id

A

hash

function

hashes

the

current

time

to

a

number

k

from

to

n

where

n

is

the

number

of

nodes

in

its

cluster

and

nodes

use

the

k

th

node

as

the

aggregator

Because

the

frequency

of

changing

the

aggregator

could

be

low

the

time

used

could

be

in

hours

or

days

therefore

the

time

only

needs

to

be

coarsely

synchronized

and

the

cluster-head

election

overhead

can

be

avoided

However

the

Dynamic

Forwarding

approach

requires

that

each

F-aggregator

knows

the

location

of

S-aggregators

of

S-clusters

that

its

F-cluster

overlaps

with

Therefore

each

time

the

S-aggregator

changes

it

has

to

notify

the

F-aggregators

To

simplify

the

cluster-head

selection

process

and

avoid

the

overhead

of

propagating

the

update

information

we

delegate

the

role

of

S-aggregators

to

F-aggregators

Instead

of

selecting

a

node

as

the

S-aggregator

and

changing

it

periodically

for

an

S-cluster

we

choose

an

F-cluster

called

Aggregating

Cluster

for

each

S-cluster

and

use

the

F-aggregator

of

the

Aggregating

Cluster

as

its

S-aggregator

The

Aggregating

Cluster

of

an

S-cluster

is

the

F-cluster

which

is

closest

to

the

sink

among

all

F-clusters

that

the

S-cluster

overlaps

with

as

shown

in

Fig.

-LRB-

a

-RRB-

assuming

that

the

sink

is

located

on

the

bottom-left

corner

Therefore

as

the

F-aggregator

changes

the

corresponding

S-aggregator

changes

as

well

When

an

F-aggregator

forwards

a

packet

to

an

S-aggregator

it

forwards

the

packet

toward

the

Aggregating

Cluster

of

that

S-aggregator

When

the

packet

reaches

the

Aggregating

Cluster

nodes

in

that

F-cluster

know

the

location

of

its

F-aggregator

and

can

forward

the

packet

to

it

Therefore

no

aggregator

update

has

to

be

propagated

to

neighboring

clusters

F-cluster

S-cluster

The

common

aggregator

for

both

the

shaded

F-cluster

and

S-cluster

-LRB-

a

-RRB-

-LRB-

b

-RRB-

F-aggregator

F-aggregator

and

st

S-aggregator

nd

S-aggregator

Figure

-LRB-

a

-RRB-

The

S-cluster

selects

the

F-cluster

closest

to

the

sink

among

its

overlapped

F-clusters

assuming

that

the

sink

is

located

at

the

bottom-left

corner

of

the

network

-LRB-

b

-RRB-

The

white

F-aggregator

selects

the

F-cluster

containing

the

gray

F-aggregator

as

the

aggregating

cluster

Now

the

role

of

S-aggregators

is

passed

on

to

the

F-aggregators

and

the

F-cluster

selected

by

an

S-aggregator

is

the

one

closer

to

the

sink

When

an

F-aggregator

wants

to

forward

packets

to

both

S-aggregators

it

selects

the

F-cluster

that

is

closer

to

itself

as

the

aggregating

cluster

of

the

first

S-aggregator

-LRB-

could

be

itself

-RRB-

to

reduce

the

number

of

transmissions

between

aggregators

as

shown

in

Fig.

-LRB-

b

-RRB-

This

selection

does

not

affect

the

property

that

packets

will

eventually

be

aggregated

at

one

aggregator

because

the

S-clusters

that

cover

the

cells

in

two

F-clusters

are

the

same

therefore

the

aggregating

cluster

selected

by

two

F-aggregators

will

be

the

same

The

benefits

of

using

this

approach

are

five-fold

First

no

leader

election

is

required

for

S-clusters

which

eliminates

the

leader

election

overhead

Second

nodes

only

need

to

know

the

F-aggregator

of

its

F-cluster

which

make

this

approach

very

scalable

Third

when

the

F-aggregator

changes

the

S-aggregator

changes

as

well

but

the

change

does

not

need

to

be

propagated

to

other

F-clusters

or

S-clusters

Fourth

if

nodes

choose

the

aggregator

by

hashing

current

time

to

get

a

node

id

of

the

aggregator

in

its

cluster

only

nodes

within

the

same

F-cluster

need

to

be

synchronized

with

each

other

And

last

since

the

Aggregating

Clusters

of

S-clusters

are

statically

computed

there

is

no

packet

overhead

for

computing

the

Aggregating

Clusters

In

this

section

we

show

that

the

maximum

distance

between

any

two

adjacent

nodes

in

ToD

only

depends

on

the

size

of

the

cells

and

is

independent

of

the

size

of

the

network

We

ignore

the

cost

from

the

aggregator

to

the

sink

since

for

perfect

aggregation

only

one

packet

will

be

forwarded

to

the

sink

from

the

aggregator

therefore

the

cost

is

comparatively

small

Compared

to

the

lower

bound

O

-LRB-

n

-RRB-

-LSB-

-RSB-

of

the

grid

network

for

a

fixed

tree

ToD

can

achieve

constant

factor

even

in

the

worst

case

u

v

s

f

u

f

v

Figure

The

worst

case

scenario

for

ToD

The

worst

case

in

ToD

is

illustrated

in

Fig.

where

only

two

adjacent

nodes

u

and

v

in

the

corner

of

two

different

F-clusters

generate

packets

and

their

F-aggregators

f

u

and

f

v

are

located

at

the

opposite

corner

We

assume

a

dense

deployment

of

sensor

nodes

therefore

the

distance

between

two

nodes

can

be

transferred

to

the

cost

of

transmitting

a

packet

between

these

nodes

Fig.

is

the

worst

case

since

if

more

nodes

are

generating

packets

in

one

cluster

it

will

only

amortize

the

cost

of

sending

packets

from

the

F-aggregator

to

the

S-aggregator

and

more

nodes

in

multiple

F-clusters

generating

packets

will

only

lower

the

average

distance

We

assume

that

the

length

of

one

side

of

the

cell

is

and

two

nodes

are

adjacent

if

their

distance

is

less

than

a

unit

of

distance

Therefore

in

Fig.

the

distance

that

packets

from

u

and

v

have

to

be

forwarded

before

they

are

aggregated

at

s

is

the

sum

of

distances

between

u

to

f

u

to

s

and

v

to

f

v

to

s

and

is

-LRB-

-RRB-

-LRB-

-RRB-

Therefore

in

the

optimal

approach

only

one

transmission

is

required

because

u

and

v

are

adjacent

In

ToD

number

of

transmission

is

required

for

the

worst

case

However

since

we

use

DAA

as

the

aggregation

technique

packets

from

adjacent

nodes

will

be

aggregated

immediately

Therefore

for

the

worst

cast

to

happen

the

distance

between

u

and

v

must

be

at

least

units

and

our

protocol

has

times

number

of

transmissions

than

optimal

The

upper

bound

is

only

dependent

on

the

size

of

a

cell

and

the

size

of

the

cell

is

dependent

on

the

size

of

an

event

This

value

is

independent

of

the

size

of

the

network

and

therefore

is

very

suitable

for

large-scale

networks

On

average

the

number

of

transmissions

will

be

much

less

than

because

first

typically

there

will

be

many

nodes

generating

packets

Second

the

distance

between

a

node

and

its

F-aggregator

is

not

always

and

the

distances

between

the

F-aggregators

and

the

S-aggregator

are

shorter

too

Third

the

DAA

approach

can

efficiently

aggregate

packets

from

adjacent

nodes

thereby

further

reducing

the

number

of

transmissions

Therefore

we

expect

the

average

distance

for

nodes

generating

packets

to

be

much

less

than

the

worst

case

In

this

section

we

use

experiments

and

simulations

to

evaluate

the

performance

of

our

semi-structured

approach

and

compare

it

with

other

protocols

Testbed

Evaluation

We

conduct

experiments

with

nodes

on

a

sensor

testbed

The

testbed

consists

of

motes

and

each

mote

is

hooked

onto

a

Stargate

The

Stargate

is

a

hardware

device

from

CrossBow

-LSB-

-RSB-

running

Linux

which

has

an

Ethernet

interface

and

a

serial

port

for

connecting

a

mote

The

Stargates

are

connected

to

the

server

using

wired

Ethernet

Therefore

we

can

program

these

motes

and

send

messages

and

signals

to

them

through

Stargates

via

Ethernet

connection

The

nodes

form

a

grid

network

with

feet

spacing

The

radio

signal

using

default

transmission

power

covers

a

lot

of

nodes

in

the

testbed

In

our

experiments

we

do

not

change

the

transmission

power

but

limit

nodes

only

to

receive

packets

from

nodes

within

two

grid

neighbors

away

i.e.

each

node

has

maximum

neighbors

We

implement

an

Anycast

MAC

protocol

on

top

of

the

MAC

layer

The

Anycast

MAC

layer

has

its

own

backoff

and

retransmission

mechanisms

and

we

disable

the

ACK

and

backoff

of

the

MAC

module

The

Anycast

MAC

implements

the

RTS-CTS-DATA-ACK

for

anycast

An

event

is

emulated

by

broadcasting

a

message

on

the

testbed

to

the

Stargates

and

the

Stargates

send

the

message

to

the

nodes

through

serial

port

The

message

contains

a

unique

ID

distinguishing

packets

generated

at

different

time

When

a

node

is

triggered

by

an

event

an

event

report

is

generated

If

the

node

has

to

delay

its

transmission

it

stores

the

packet

in

a

report

queue

Both

the

application

layer

and

Anycast

MAC

layer

can

access

the

queue

therefore

they

can

check

if

the

node

has

packets

for

aggregation

or

aggregate

the

received

packets

to

packets

in

the

queue

First

we

evaluate

the

following

protocols

on

the

testbed

and

the

codes

are

available

on-line

Dynamic

Forwarding

over

ToD

-LRB-

ToD

-RRB-

The

semi-structured

approach

we

proposed

in

this

paper

DAA

is

used

to

aggregate

packets

in

each

F-cluster

and

aggregated

packets

are

forwarded

to

the

sink

on

ToD

Data

Aware

Anycast

-LRB-

DAA

-RRB-

The

structure-less

approach

proposed

in

-LSB-

-RSB-

Shortest

Path

Tree

-LRB-

SPT

-RRB-

Nodes

send

packets

to

the

sink

through

the

shortest

path

tree

immediately

after

sensing

an

event

Aggregation

is

opportunistic

and

happens

only

if

two

packets

are

at

the

same

node

at

the

same

time

The

shortest

path

tree

is

constructed

immediately

after

the

network

is

deployed

A

message

is

broadcast

from

the

sink

and

flooded

into

the

network

to

create

a

shortest

path

tree

from

all

nodes

to

the

sink

Shortest

Path

Tree

with

Fixed

Delay

-LRB-

SPT-D

-RRB-

Same

as

the

SPT

approach

but

nodes

delay

their

transmission

according

to

their

height

in

the

tree

to

wait

for

packets

from

their

children

Due

to

the

scale

of

the

testbed

in

ToD

we

only

divide

the

network

into

two

F-clusters

which

forces

the

smallest

cell

to

have

only

sensor

nodes

However

we

do

not

limit

the

size

of

an

event

to

be

smaller

than

the

cell

size

The

event

size

is

larger

than

the

cell

size

in

all

following

experiments

We

use

the

normalized

number

of

transmissions

as

the

metric

to

compare

the

performance

of

these

protocols

The

normalized

number

of

transmissions

is

the

average

number

of

transmissions

performed

in

the

entire

network

to

deliver

one

unit

of

useful

information

from

sources

to

the

sink

It

can

be

converted

to

the

normalized

energy

consumption

if

we

know

the

sending

and

receiving

cost

of

one

transmission

therefore

the

energy

spent

on

data

collection

for

one

packet

can

be

derived

We

do

not

consider

energy

consumption

on

idle

listening

here

since

all

nodes

are

fully

active

for

all

protocols

in

the

experiments

and

simulations

and

the

idle

energy

consumption

would

be

similar

for

all

protocols

To

reduce

the

energy

consumption

on

idle

listening

various

duty

cycling

protocols

have

been

proposed

However

due

to

the

page

limitation

we

are

unable

to

describe

how

to

integrate

those

works

Fig.

shows

the

normalized

number

of

transmissions

for

different

event

sizes

We

fixed

the

location

of

the

event

and

vary

its

diameter

from

ft

to

ft

where

nodes

within

two

grid-hops

to

six

grid-hops

of

the

event

will

be

triggered

respectively

and

send

packets

to

the

sink

located

at

one

corner

of

the

network

We

use

seconds

as

maximum

delay

for

all

protocols

except

SPT

For

event

size

less

than

ft

there

are

too

little

nodes

been

triggered

-LRB-

less

than

five

-RRB-

and

all

triggered

nodes

are

within

transmission

range

Data

aggregation

is

not

so

interesting

in

such

scenario

therefore

we

do

not

evaluate

it

Actually

DAA

can

perform

best

since

all

packets

can

be

aggregated

because

all

triggered

nodes

are

within

transmission

range

of

each

other

All

protocols

have

better

performance

when

the

size

of

the

event

increases

because

packets

have

more

chances

of

being

aggregated

ToD

performs

best

among

all

protocols

in

all

scenarios

This

shows

that

DAA

can

efficiently

achieve

early

aggregation

and

the

Dynamic

Forwarding

over

ToD

can

effectively

reduce

the

cost

of

directly

forwarding

unaggregated

packets

to

the

sink

in

DAA

In

SPT-D

when

the

event

size

is

smaller

the

long

stretch

effect

is

more

significant

than

in

larger

event

scenario

When

event

size

is

large

for

example

two-third

of

nodes

in

the

network

are

triggered

when

the

diameter

of

the

event

is

feet

most

of

the

packets

can

be

aggregated

to

their

parent

with

one

transmission

This

indicates

that

in

applications

where

most

nodes

are

transmitting

the

fixed

structure

such

as

SPT-D

is

better

but

when

only

a

small

subset

of

nodes

are

transmitting

their

performance

degrades

because

of

the

long

stretch

problem

We

notice

that

the

variance

of

some

results

in

SPT

and

SPT-D

is

very

high

For

example

when

the

event

size

is

feet

in

diameter

the

maximum

normalized

number

of

Normalized

Number

of

Transmissions

Event

Size

-LRB-

ft

-RRB-

ToD

DAA

SPT

SPT-D

Figure

The

normalized

number

of

transmissions

for

different

event

sizes

from

experiments

on

sensors

missions

in

SPT-D

is

and

the

minimum

value

is

By

tracing

into

the

detail

experiment

logs

we

found

that

the

high

variance

is

because

of

the

different

shortest

path

trees

The

tree

is

re-constructed

for

each

experiment

and

therefore

may

change

from

experiment

to

experiment

We

found

that

SPT-D

always

gets

better

performance

in

one

tree

where

all

sources

are

under

the

same

subtree

and

performs

badly

in

the

other

tree

where

sources

are

located

under

two

or

three

different

subtrees

This

further

supports

our

claims

that

the

long

stretch

problem

in

fixed

structured

approaches

affects

their

performance

significantly

The

second

experiment

evaluates

the

performance

of

these

protocols

for

different

values

of

maximum

delay

We

vary

the

delay

from

to

seconds

and

all

nodes

in

the

network

generate

one

packet

every

seconds

Fig.

shows

the

results

As

we

described

the

performance

of

the

structure-based

approaches

heavily

depends

on

the

delay

The

SPT-D

performs

worse

than

ToD

when

the

maximum

delay

is

less

than

five

seconds

and

the

performance

increases

as

the

delay

increases

On

the

contrary

the

performance

of

ToD

and

DAA

does

not

change

for

different

delays

which

is

different

from

results

observed

in

-LSB-

-RSB-

We

believe

that

this

is

because

with

the

default

transmission

power

a

large

number

of

nodes

are

in

interference

range

when

nodes

transmit

Therefore

even

if

nodes

do

not

delay

their

transmissions

only

one

node

can

transmit

at

any

given

time

Other

nodes

will

be

forced

to

delay

which

has

the

same

effect

as

the

Randomized

Waiting

Large

Scale

Simulation

To

evaluate

and

compare

the

performance

and

scalability

of

ToD

with

other

approaches

requires

a

large

sensor

network

which

is

currently

unavailable

in

real

experiments

Therefore

we

resort

to

simulations

In

this

section

we

use

the

network

simulator

to

evaluate

these

protocols

Besides

ToD

DAA

and

SPT

we

evaluate

OPT

Optimal

Aggregation

Tree

to

replace

the

SPT-D

protocol

In

OPT

nodes

forward

their

packets

on

an

aggregation

tree

rooted

at

the

center

of

the

event

Nodes

know

where

to

forward

packets

to

and

how

long

to

wait

The

tree

is

constructed

in

advance

and

changes

when

the

event

moves

assuming

the

location

and

mobility

of

the

event

are

known

Normalized

Number

of

Transmissions

Maximum

Delay

-LRB-

s

-RRB-

ToD

DAA

SPT

SPT-D

Figure

The

normalized

number

of

transmissions

for

different

maximum

delays

from

experiments

on

sensors

Ideally

only

n

transmissions

are

required

for

n

sources

This

is

the

lower

bound

for

any

structure

therefore

we

use

it

as

the

optimal

case

This

approach

is

similar

to

the

aggregation

tree

proposed

in

-LSB-

-RSB-

but

without

its

tree

construction

and

migration

overhead

We

do

not

evaluate

SPT-D

in

simulation

because

SPT-D

is

not

practical

in

the

large

scale

network

In

the

largest

simulation

scenario

the

network

is

a

network

According

to

the

simulation

in

smaller

network

SPT-D

gets

best

performance

when

the

delay

of

each

hop

is

about

seconds

This

makes

nodes

closer

to

the

sink

have

about

seconds

delay

in

SPT-D

which

is

not

advisable

We

perform

simulations

of

these

protocols

on

a

grid

network

with

node

separation

therefore

there

are

a

total

of

nodes

in

the

network

The

data

rate

of

the

radio

is

Kbps

and

the

transmission

range

of

the

nodes

is

slightly

higher

than

An

event

moves

in

the

network

using

the

random

way-point

mobility

model

at

the

speed

of

s

for

seconds

The

event

size

is

in

diameter

The

nodes

triggered

by

an

event

will

send

packets

every

five

seconds

to

the

sink

located

at

-LRB-

-RRB-

The

aggregation

function

evaluated

here

is

perfect

aggregation

i.e.

all

packets

can

be

aggregated

into

one

packet

without

increasing

the

packet

size

Event

Size

We

first

evaluate

the

performance

for

these

protocols

on

different

number

of

nodes

generating

the

packets

This

simulation

reflects

the

performance

of

each

protocol

for

different

event

sizes

We

study

the

performance

for

mobility

scenarios

and

show

the

average

maximum

and

minimum

values

of

the

results

Fig.

-LRB-

a

-RRB-

shows

the

result

of

normalized

number

of

transmissions

ToD

improves

the

performance

of

DAA

and

SPT

by

and

and

is

higher

than

OPT

However

OPT

has

the

best

performance

by

using

the

aggregation

tree

that

keeps

changing

when

event

moves

but

its

overhead

is

not

considered

in

the

simulation

SPT

has

very

poor

performance

since

its

aggregation

is

opportunistic

Except

the

SPT

the

performance

of

all

other

protocols

is

quite

steady

This

shows

that

they

are

quite

scalable

in

terms

of

the

event

size

Fig.

-LRB-

b

-RRB-

and

-LRB-

c

-RRB-

show

the

total

number

of

transmissions

and

total

units

of

useful

information

received

by

the

sink

As

observed

in

-LSB-

-RSB-

DAA

and

ToD

have

higher

number

of

received

packets

than

OPT

due

to

the

ability

of

structure-less

aggregation

to

aggregate

packets

early

and

scatter

them

away

from

each

other

to

reduce

contention

ToD

performs

better

than

DAA

in

terms

of

the

normalized

number

of

transmissions

because

of

its

ability

to

aggregate

packets

at

nodes

closer

to

the

source

and

thus

it

reduces

the

cost

of

forwarding

packets

from

sources

to

the

sink

Scalability

In

this

set

of

simulations

we

evaluate

the

scalability

of

our

protocol

since

our

goal

is

to

design

a

scalable

data

aggregation

protocol

If

a

protocol

is

not

scalable

its

performance

will

degrade

as

the

size

of

the

network

increases

To

evaluate

the

scalability

of

a

protocol

we

limit

an

event

to

move

only

in

a

bounded

region

at

a

certain

distance

from

the

sink

to

simulate

the

effect

of

different

network

sizes

We

limit

an

event

to

move

within

a

rectangle

and

change

the

distance

of

the

rectangle

to

the

sink

from

to

as

shown

in

Fig.

In

order

to

be

fair

to

all

scenarios

we

limit

the

event

not

to

move

closer

than

to

the

network

boundary

such

that

the

number

of

nodes

triggered

by

the

event

does

not

change

drastically

Figure

The

simulation

scenario

for

scalability

The

event

is

limited

to

move

only

within

a

small

gray

rectangle

in

each

simulation

Fig.

shows

the

results

of

the

scalability

simulation

The

performance

of

ToD

and

OPT

remains

steady

and

ToD

is

higher

than

OPT

This

shows

that

ToD

is

quite

scalable

as

its

performance

does

not

degrade

as

the

size

of

the

network

increases

The

performance

of

both

DAA

and

SPT

degrades

as

the

size

of

the

network

increases

The

normalized

number

of

transmissions

for

DAA

and

SPT

doubled

when

the

event

moves

from

the

closest

rectangle

-LRB-

to

the

sink

-RRB-

to

the

farthest

rectangle

Fig.

-LRB-

c

-RRB-

shows

the

number

of

packets

received

at

the

sink

per

event

If

all

packets

can

be

aggregated

near

the

event

and

forwarded

to

the

sink

the

sink

will

receive

only

one

packet

Conversely

more

packets

received

at

the

sink

shows

that

fewer

aggregations

happened

in

the

network

The

cost

of

forwarding

more

packets

to

the

sink

increases

rapidly

as

the

size

of

the

network

increases

We

can

see

that

in

both

DAA

and

SPT

the

sink

receives

many

packets

Though

the

number

of

packets

received

at

the

sink

remains

quite

steady

the

total

number

of

transmissions

increases

linearly

as

the

distance

from

the

sources

to

the

sink

increases

Ideally

the

number

of

received

packets

at

sink

is

if

all

packets

can

be

aggregated

at

the

aggregator

However

the

number

of

received

packets

at

sink

is

higher

than

in

ToD

Normalized

Number

of

Transmissions

Event

Size

-LRB-

m

-RRB-

ToD

DAA

SPT

OPT

Number

of

Total

Transmissions

Event

Size

-LRB-

m

-RRB-

ToD

DAA

SPT

OPT

Unit

of

Received

Information

Event

Size

-LRB-

m

-RRB-

ToD

DAA

SPT

OPT

-LRB-

a

-RRB-

Normalized

number

of

transmissions

-LRB-

b

-RRB-

Number

of

transmissions

-LRB-

c

-RRB-

Unit

of

received

information

Figure

The

simulation

results

for

different

event

sizes

and

OPT

This

is

because

the

delay

in

CSMA-based

MAC

protocol

can

not

be

accurately

predicted

therefore

the

aggregator

might

send

the

packet

to

the

sink

before

all

packets

are

forwarded

to

it

Though

the

cost

of

forwarding

the

unaggregated

packets

from

aggregator

to

the

sink

in

ToD

and

OPT

also

increases

when

the

size

of

the

network

increases

the

increase

is

comparably

smaller

than

DAA

and

SPT

because

few

packets

are

forwarded

to

the

sink

without

aggregation

We

observe

that

the

number

of

received

packets

at

the

sink

in

ToD

is

higher

when

the

event

is

closer

to

the

sink

In

our

simulation

nodes

in

the

same

F-cluster

as

the

sink

will

always

use

sink

as

the

F-aggregator

because

we

assume

that

the

sink

is

wire

powered

therefore

there

is

no

need

to

delegate

the

role

of

aggregator

to

other

nodes

in

order

to

evenly

distribute

the

energy

consumption

Cell

Size

The

above

simulations

use

the

maximum

size

of

an

event

as

the

cell

size

As

we

described

in

Section

this

ensures

that

the

Dynamic

Forwarding

can

aggregate

all

packets

at

an

S-aggregator

and

the

cost

of

forwarding

the

aggregated

packets

to

the

sink

is

minimized

However

large

cell

size

increases

the

cost

of

aggregating

packets

to

the

aggregator

as

we

use

DAA

as

the

aggregation

technique

in

an

F-cluster

In

this

section

we

evaluate

the

impact

of

the

size

of

a

cell

on

the

performance

of

ToD

We

vary

the

cell

size

from

to

and

run

simulations

for

three

different

event

sizes

which

are

and

in

diameter

The

results

are

collected

from

five

different

event

mobility

patterns

and

shown

in

Fig.

When

the

size

of

cell

is

larger

than

the

event

size

the

performance

is

worse

because

the

cost

of

aggregating

packets

to

F-aggregator

increases

but

the

cost

of

forwarding

packets

from

S-aggregator

does

not

change

When

the

size

of

cell

is

too

small

the

cost

of

forwarding

packets

to

sink

increases

because

packets

will

be

aggregated

at

different

F-aggregators

and

more

packets

will

be

forwarded

to

the

sink

without

further

aggregation

In

general

when

the

size

of

the

F-cluster

is

small

enough

to

only

contain

one

node

or

when

the

size

of

the

F-cluster

is

large

enough

to

include

all

nodes

in

the

network

ToD

just

downgrades

to

DAA

ToD

has

the

best

performance

when

the

cell

size

is

-LRB-

F-cluster

size

is

-RRB-

when

the

event

size

is

in

diameter

When

the

diameter

of

an

event

is

and

using

as

the

cell

size

has

the

best

performance

-LRB-

F-cluster

size

is

-RRB-

This

shows

that

the

ToD

performance

can

be

further

optimized

by

selecting

the

appropriate

cell

size

To

explore

the

relation

between

the

event

and

cell

size

for

optimization

will

be

part

of

our

future

work

In

this

paper

we

propose

a

semi-structured

approach

that

locally

uses

a

structure-less

technique

followed

by

Dynamic

Forwarding

on

an

implicitly

constructed

packet

forwarding

structure

ToD

to

support

network

scalability

ToD

avoids

the

long

stretch

problem

in

fixed

structured

approaches

and

eliminates

the

overhead

of

construction

and

maintenance

of

dynamic

structures

We

evaluate

its

performance

using

real

experiments

on

a

testbed

of

sensor

nodes

and

simulations

on

node

networks

Based

on

our

studies

we

find

that

ToD

is

highly

scalable

and

it

performs

close

to

the

optimal

structured

approach

Therefore

it

is

very

suitable

for

conserving

energy

and

extending

the

lifetime

of

large

scale

sensor

networks

-LSB-

-RSB-

W.

Heinzelman

A.

Chandrakasan

and

H.

Balakrishnan

Energy-Efficient

Communication

Protocol

for

Wireless

Microsensor

Networks

in

Proceedings

of

the

Annual

Hawaii

International

Conference

on

System

Sciences

vol

January

-LSB-

-RSB-

W.

Heinzelman

A.

Chandrakasan

and

H.

Balakrishnan

An

Application-Specific

Protocol

Architecture

for

Wireless

Microsensor

Networks

in

IEEE

Transactions

on

Wireless

Communications

vol

October

pp.

-LSB-

-RSB-

C.

Intanagonwiwat

D.

Estrin

and

R.

Goviindan

Impact

of

Network

Density

on

Data

Aggregation

in

Wireless

Sensor

Networks

in

Technical

Report

University

of

Southern

California

November

-LSB-

-RSB-

W.

Zhang

and

G.

Cao

Optimizing

Tree

Reconfiguration

for

Mobile

Target

Tracking

in

Sensor

Networks

in

Proceedings

of

INFOCOM

vol

March

pp.

Normalized

Number

of

Transmissions

Distance

to

the

Sink

-LRB-

m

-RRB-

ToD

DAA

SPT

OPT

Normalized

Number

of

Transmissions

Distance

to

the

Sink

-LRB-

m

-RRB-

ToD

DAA

OPT

Number

of

Received

Packets

Distance

to

the

Sink

-LRB-

m

-RRB-

ToD

DAA

SPT

OPT

-LRB-

a

-RRB-

Normalized

number

of

transmission

-LRB-

b

-RRB-

Zoom

in

of

Fig.

-LRB-

a

-RRB-

-LRB-

c

-RRB-

Number

of

received

packets

Figure

The

simulation

results

for

difference

distances

from

the

event

to

the

sink

Normalized

Number

of

Transmissions

Cell

Size

-LRB-

m

-RRB-

Number

of

Total

Transmissions

Cell

Size

-LRB-

m

-RRB-

Number

of

Received

Packets

Cell

Size

-LRB-

m

-RRB-

-LRB-

a

-RRB-

Normalized

number

of

transmissions

-LRB-

b

-RRB-

Number

of

transmissions

-LRB-

c

-RRB-

Number

of

received

packets

Figure

The

simulation

results

for

difference

cell

sizes

-LSB-

-RSB-

W.

Zhang

and

G.

Cao

DCTC

Dynamic

Convoy

Tree-based

Collaboration

for

Target

Tracking

in

Sensor

Networks

in

IEEE

Transactions

on

Wireless

Communications

vol

September

pp.

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-RSB-

M.

Ding

X.

Cheng

and

G.

Xue

Aggregation

Tree

Construction

in

Sensor

Networks

in

Proceedings

of

the

IEEE

Vehicular

Technology

Conference

vol

October

pp.

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Luo

J.

Luo

and

Y.

Liu

Energy

Efficient

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with

Adaptive

Data

Fusion

in

Sensor

Networks

in

Proceedings

of

the

Third

ACM/SIGMOBILEe

Workshop

on

Foundations

of

Mobile

Computing

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A.

Goel

and

D.

Estrin

Simultaneous

Optimization

for

Concave

Costs

Single

Sink

Aggregation

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Single

Source

Buy-at-Bulk

in

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Annual

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Symposium

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Implementation

of

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and

J.

Polastre

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Dutta

and

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the

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Lenstra

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and

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B.

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The

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Guided

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Cristescu

B.

Beferull-Lozano

and

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W.

Fan

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in

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in

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of

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Y.

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and

R.

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Energy

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Useable

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in

Correlation

Aware

Data

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in

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Second

Annual

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and

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S.

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C.

Intanagonwiwat

R.

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A

Scalable

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Robust

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D.

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