Optimal computation of symmetric Boolean functions in tree networks Conference Paper uri icon

abstract

  • In this paper, we address the scenario where nodes with sensor data are connected in a tree network, and every node wants to compute a given symmetric Boolean function of the sensor data. We first consider the problem of computing a function of two nodes with integer measurements. We allow for block computation to enhance data fusion efficiency, and determine the minimum worst-case total number of bits to be exchanged to perform the desired computation. We establish lower bounds using fooling sets, and provide a novel scheme which attains the lower bounds, using information theoretic tools. For a class of functions called sum-threshold functions, this scheme is shown to be optimal. We then turn to tree networks and derive a lower bound for the number of bits exchanged on each link by viewing it as a two node problem. We show that the protocol of recursive in-network aggregation achieves this lower bound in the case of sum-threshold functions. Thus we have provided a communication and in-network computation strategy that is optimal for each link. All the results can be extended to the case of non-binary alphabets. In the case of general graphs, we present a cut-set lower bound, and an achievable scheme based on aggregation along trees. For complete graphs, the complexity of this scheme is no more than twice that of the optimal scheme. © 2010 IEEE.

name of conference

  • 2010 IEEE International Symposium on Information Theory - ISIT

published proceedings

  • 2010 IEEE International Symposium on Information Theory

author list (cited authors)

  • Kowshik, H., & Kumar, P. R

citation count

  • 8

complete list of authors

  • Kowshik, Hemant||Kumar, PR

publication date

  • June 2010

publisher