Wireless coverage with disparate ranges

Abstract

One of the most fundamental task of wireless networks is to provide coverage of a set of targets. Suppose that all nodes and targets lie in a plane, and all nodes have circular coverage ranges of arbitrary radii. The problem Minimum Wireless Cover (MWC) seeks the fewest nodes to cover the targets. If all nodes are associated with some positive prices, the problem Cheapest Wireless Cover (CWC) seeks a cheapest set of nodes to cover the targets. If all nodes have bounded lives, the problem Max-Life Wireless Cover (MLWC) seeks wireless coverage schedule of maximum life subject to the life constraints of individual nodes. In this paper, we present a polynomial time approximation scheme (PTAS) for MWC, and two randomized 2O(log* n)-approximation algorithms for CWC and MLWC respectively, where n is the number of nodes, and log* n is the iterated logarithm of n with base 2.