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.