Solving the k-center Problem Efficiently with a Dominating Set Algorithm

Abstract

We present a polynomial time heuristic algorithm for the minimum dominating set problem. The algorithm can readily be used for solving the minimum α -all-neighbor dominating set problem and the minimum set cover problem. We apply the algorithm in heuristic solving the minimum k-center problem in polynomial time. Using a standard set of 40 test problems we experimentally show that our k-center algorithm performs much better than other well-known heuristics and is competitive with the best known (non-polynomial time) algorithms for solving the k-center problem in terms of average quality and deviation of the results as well as the execution time.

Bandwidth Optimization for Multicast Transmissions in Virtual Circuit Networks

“…In all experiments, to determine the location of the diffusing nodes in G we use a k-center heuristic algorithm based on a dominating set algorithm [16]. This approach was chosen because the k-center algorithm distributes the centers "equally" in the graph.…”

Selection of time synchronizing nodes in wireless sensor network

“…One of the approaches for solving the dominating set problem is the heuristic algorithm given in [9]. In this algorithm, the dominating set D grows according to the "lazy" principle, i.e.…”

“…We have implemented the algorithm in [9] for minimum dominating set and algorithm in [14] for minimum kdominating set and used their results to obtain synchronization nodes in non fault tolerant settings and fault tolerant settings, respectively. The selection of nodes has been evaluated with respect to various metrics.…”

“…Since this problem is NP-Complete, we use approximation algorithms for solving minimum dominating set problem viz. Random, Greedy, and a heuristic based [9] algorithm to obtain a solution for selecting synchronizing nodes.…”

p-Center Problems

“…They concluded that these two classes of spanning trees do not always include the optimizing tree, but they do in most of the instances. Mihelič and Robič (2005) solved the vertex-restricted p-center problem by introducing a heuristic algorithm based on solving a finite series of minimum dominating set problems. Given a graph G D .V; E/, the minimum dominating set problem aims to find a node subset S V of minimum cardinality so that any node in V n S is adjacent to some node in S .…”