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 Khuller Department of Computer Science, University of Maryland, College Park. Outline. Introduction Compression tree problem Prior approaches Approximation algorithm - PowerPoint PPT PresentationTRANSCRIPT
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.