Efficient Construction of Dominating Set in Wireless Networks [article]

Xiaohua Xu, Xiang-Yang Li
2012 arXiv   pre-print
Considering a communication topology of a wireless network modeled by a graph where an edge exists between two nodes if they are within each other's communication range. A subset U of nodes is a dominating set if each node is either in U or adjacent to some node in U. Assume each node has a disparate communication range and is associated with a positive weight, we present a randomized algorithm to find a min-weight dominating set. Considering any orientation of the graph where an arc uv exists
more » ... f the node v lies in u's communication range. A subset U of nodes is a strongly dominating set if every node except U has both in-neighbor(s) and out-neighbor(s) in U. We present a polynomial-time algorithm to find a strongly dominating set of size at most (2+ϵ) times of the optimum. We also investigate another related problem called K-Coverage. Given are a set D of disks with positive weight and a set P of nodes. Assume all input nodes lie below a horizontal line l and all input disks lie above this line l in the plane. The objective is to find a min-weight subset D'⊆ D of disks such that each node is covered at least K disks in D'. We propose a novel two-approximation algorithm for this problem.
arXiv:1208.5738v1 fatcat:v7kbyz2hczfkvn2hubcegbhc2m