on computing compression trees for data collection in wireless sensor networks
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On Computing Compression Trees for Data Collection in Wireless Sensor Networks
Jian Li, Amol Deshpande and Samir KhullerDepartment of Computer Science,
University of Maryland, College Park
Outline
• Introduction– Compression tree problem
• Prior approaches• Approximation algorithm• Experimental results• Conclusion
IntroductionDistributed Source Coding (DSC)
• Distributed source coding: Slepian–Wolf coding– Allow nodes to use joint coding of correlated data
without explicit communication– the total amount of data transmitted for a multi-hop
network
– DSC requires perfect knowledge of the correlations among the nodes, and may return wrong answers if the observed data values deviate from what is expected.
– Optimal transmission structure: Shortest path tree
Introduction
• Encoding with explicit communication Pattem et al. [7], Chu et al. [8], Cristescu et al. [9]– exploit the spatio-temporal correlations through
explicit communication among the sensor nodes.– These protocols may exploit only a subset of the
correlations– Without knowing the correlation among nodes a
priori.
ProblemOptimal Compression Tree Problem
• Given a given communication topology and a given set of correlations among the sensor nodes, find an optimal compression tree that minimizes the total communication cost
• Assumption:– utilize only second-order marginal or conditional probability distributions – only directly utilize pairwise correlations between the sensor nodes.
Prior ApproachesIND
Prior ApproachesCluster
Prior ApproachesDSC
Prior ApproachesCompression Tree
Communication Cost• Necessary Communication (NC):
=
• Intra-source Communication (IC):IC cost = Total Cost – NC cost = (6+3) - (4+5)
= 2 - 2
Solution Space
• Subgraphs of G (SG)– compress Xi using Xj only if i and j are neighbors.
• The WL-SG Model: Uniform Entropy and Conditional Entropy Assumption– Assume that H(Xi) = 1, i, and H(Xi|Xj) = , for all
adjacent pairs of nodes (Xi, Xj).• Weakly Connected Dominating Set (WCDS)
Problem
WL-SG Model
The approach for the CDS problem that gives a 2H , approximation [19], gives a H +1 approximation for WCDS [20].
The Generic Greedy Framework
• The main algorithm greedily constructs a compression tree by greedily choosing subtrees to merge in iterations.
The Generic Greedy Framework
• Step 1: – start with a empty graph F1 that consists of only isolated
nodes.• Step 2 (iteration): – In each iteration, we combine some trees together into a
new larger tree by choosing the most cost-effective treestar
• Step 3: – terminates when only one tree is left
r
The Generic Greedy Framework
Approximation factor
Experimental Results
• Rainfall Data:– we use an analytical expression of the entropy
that was derived by Pattem et al. [7] for a data set containing precipitation data collected in the states of Washington and Oregon during 1949-1994.
Rainfall Data:
Intel Lab Data:
Conclusion• This paper addressed the problem of finding an optimal or a near-
optimal compression tree for a given sensor network: – a compression tree is a directed tree over the sensor network nodes such
that the value of a node is compressed using the value of its parent.• We draw connections between the data collection problem and
weakly connected dominating sets, – we use this to develop novel approximation algorithms for the problem.
• We present comparative results on several synthetic and real-world datasets – showing that our algorithms construct near-optimal compression trees
that yield a significant reduction in the data collection cost.
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