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 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
gg
g
10
88
5
810
8
58
5
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
5
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
4000
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.