Rate-based Data Propagation in Sensor Networks

Gurdip Singh and Sandeep PujarComputing and Information Sciences

Sanjoy DasElectrical and Computer Engineering

Kansas State University

WCNC 2004Speaker: Hao-Chun Sun

Outline Introduction Rate-based Tree (RBT) Algorithm

Breadth-First tree based algorithm (BFS) Single phase Algorithm (SPA)

Performance Evaluation Conclusion and Future Work

Introduction -background-

Sensor networks Small and cheap computational nodes Such nodes can sense and communication data to

potential consumer nodes. Monitor traffic movements Application

One or one more operators may be interested in queries.

Different operators may be interested in knowing this information at different sampling rates.

Introduction -motivation-

The problem of constructing rate-based trees (RBT) A single source s and a set of destination D Each d in D specifies the rate rd

To construct an optimal multicast tree with s as the root such that each destination gets data at the desired rate.

Optimal multicast tree has the lowest cost. NP-complete problem

Rate-based Tree (RBT) Algorithm Several variants of the general problem

Un-weight graphs Breadth-First Tree based algorithm (BFS) Single phase algorithm (SPA)

Weight graphs SPA_W algorithm

Rate-based Tree (RBT) Algorithm RBT Problem Definition

Network: G=(N,E) N: nodes E: edges, representing the communication links

A single source node s and a set of destinations D Destination i is interested in obtaining information at r

ate ri from the source.

All nodes are destinations

Rate-based Tree (RBT) Algorithm RBT Problem Definition

RBT must to satisfy two properties For each node i with parent edge e, re r≧ i

For each node i, the rate assigned to its parent edge must be greater than or equal to ri and the rate of any of its outgoing edges.

Pi

iri

re

ro1

ro2

Rate-based Tree (RBT) Algorithm An example of rate-based Trees

g

a

b c

d

e

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10 8

5

5

0

0

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8

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Rate-based Tree (RBT) Algorithm An example of rate-based Trees

g

a

b c

d

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10 8

5

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0

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85

8

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Rate-based Tree (RBT) Algorithm Two metric to evaluate the algorithms

The cost of the RBT The sum of the cost of all tree edges

Cost = w (i, j) × re, where e is the edge from i to j.

The number of messages sent in and execution of the algorithm.

g

gg

g

g

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10

88

5

810

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Cost (A)=10+8+8+8+5Cost (B)=10+8+8+5+5

Cost (A)=10+8+8+8+5Cost (B)=10+8+8+5+5

(A) (B)

Rate-based Tree (RBT) Algorithm Un-weighted graphs

Breadth-First Tree based algorithm (BFS)— BFS tree construction algorithm

Along the path to the root is shortest path for un-weighted graphs

Sum of the weight along the path to the root is minimal for weighted graphs.

Label the edges rules

Rate-based Tree (RBT) Algorithm Un-weighted graphs

Breadth-First Tree based algorithm (BFS)—a

b

e

c

d

520

40

20

label(20)label(40)

label(20)

label(40)20

20

40

40

a

b

e

c

d

520

40

20

label(20)

label(40)

label(5)

label(40)5

20

40

40

Rate-based Tree (RBT) Algorithm Un-weighted graphs

A Single Phase Algorithm (SPA)—

a

f

d

b c

e

5

10

5

510

explore(0)

explore(0)

explore(0)

explore(5)

Ack(5)

Ack(5) Ack(10)

explore(5)

Ack(10)explore(10)

Ack(10)

explore(5)

Ack(5)

update(10)

5

5

5

10

10

1010

10update(10)

Nack

Rate-based Tree (RBT) Algorithm Un-weighted graphs

A Single Phase Algorithm (SPA)—

a

f

d

b c

e

5

10

5

510

10

5

10

10

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Rate-based Tree (RBT) Algorithm Weighted graphs

SPA_W algorithm— Modify switching parent rules

When node i receive an explore (r) message form j. r r≧ i and r > rpi

ri × cost (i, j) < ri × cost (i, Pi)

j

i

Piexplore(r)

cost (i, j)cost (i, j) cost (i, Pi)cost (i, Pi)

Performance Evaluation Discrete event simulation Network Topologies were generated by

randomly placing N nodes in a M×M matrix. The probability of two nodes being

neighboring is inversely proportional to the distance between them.

N is ranging from 20 to 160.

Performance Evaluation Tree cost for SPA vs. BFS

0

500

1000

1500

2000

10 20 40 80 160

Number of Nodes

Tre

e Cos

t

BFS

SPA

Performance Evaluation Number of messages for SPA vs. BFS

0

500010000

1500020000

2500030000

35000

10 20 40 80 160

Number of Nodes

Num

ber of

mes

sage

s BFS

SPA

Performance Evaluation Number of messages for different rate groups

0

1000

2000

3000

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5000

8 6 4 2 1

Different rate groups R

Num

ber of

mes

sage

s

BFS

SPA

Performance Evaluation Weighted Tree Cost

0

20000

40000

60000

80000

10 20 40 80 160

Number of Nodes

Wei

ghte

d Tre

e Cos

t BFS

SPA

SPA_W

Conclusion and Future Work This paper presented algorithms for rate-

based propagation of data in sensor network. The paper addresses the problems where

consumers of data may be requesting the data from the same source at different rates and needing to construct a data propagation tree that satisfies all requested rate.

It presented an efficient algorithm and studied several of its variants.

Conclusion and Future Work We will consider the case of internal nodes

are not destination nodes. An interesting variation is the case when are

multiple data items and multiple producers and the consumers in obtaining data items.

We plan to study dynamic changes to the rates at which consumers are subscribing.