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 Experimental results Conclusion

Introduction Distributed 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.

Problem Optimal 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 Approaches IND

Prior Approaches Cluster

Prior Approaches DSC

Prior Approaches Compression Tree

Communication Cost Necessary Communication (NC): = Intra-source Communication (IC): IC cost = Total Cost – NC cost = (6+3  ) - (4+5  ) = 

Solution Space Subgraphs of G (SG) – compress X i using X j only if i and j are neighbors. The WL-SG Model: Uniform Entropy and Conditional Entropy Assumption – Assume that H(X i ) = 1,  i, and H(X i |X j ) = , 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

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.