Optimal ordering of transmissions for computing Boolean threshold functions Conference Paper uri icon

abstract

  • We address a sequential decision problem that arises in the computation of symmetric Boolean functions of distributed data. We consider a collocated network, where each node's transmissions can be heard by every other node. Each node has a Boolean measurement and we wish to compute a given Boolean function of these measurements. We suppose that the measurements are independent and Bernoulli distributed. Thus, the problem of optimal computation becomes the problem of optimally ordering nodes' transmissions so as to minimize the total expected number of bits. We solve the ordering problem for the class of Boolean threshold functions. The optimal ordering is dynamic, i.e., it could potentially depend on the values of previously transmitted bits. Further, it depends only on the ordering of the marginal probabilites, but not on their exact values. This provides an elegant structure for the optimal strategy. For the case where each node has a block of measurements, the problem is significantly harder, and we conjecture the optimal strategy. © 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

  • 3

complete list of authors

  • Kowshik, Hemant||Kumar, PR

publication date

  • June 2010

publisher