Decentralized Message Passing for Minimum Sensor Cover Based on Belief Propagation

Abstract

In this paper, decentralized message passing is addressed for a placement problem, named the minimum sensor cover problem: given point-wise tasks and sensors with omnidirectional coverage, find the minimum set of sensors that cover all the tasks. The minimum sensor cover problem can be converted to the geometric set cover by discretization of the solution space of the problem, and the geometric set cover is formulated as a maximum a posteriori (MAP) state assignment problem in a pairwise Markov random field model, which is a particular type of graphical models representing dependency relations between statistical variables. Belief propagation algorithm is a local iterative message passing algorithm devised to solve statistical inference problems in graphical models, but in a MAP assignment formulation of the set cover problem, solutions of belief propagation do not always result in convergence and the algorithm even produces infeasible solutions in largesized problems. A message passing algorithm based on belief propagation is presented to obtain stable and guaranteed feasible solutions by decentralized computations and numerical simulation validates the convergence, feasibility, and preferable solution quality of the presented algorithm against existing modifications of belief propagation and centralized greedy algorithm for the set cover.