Minimum Weight Dominating Set Problem Research Articles

A [formula omitted]-approximation algorithm for minimum weighted dominating set in unit disk graph

We study the minimum weight dominating set problem in weighted unit disk graph, and give a polynomial time algorithm with approximation ratio 5 + ϵ , improving the previous best result of 6 + ϵ in [Yaochun Huang, Xiaofeng Gao, Zhao Zhang, Weili Wu, A better constant-factor approximation for weighted dominating set in unit disk graph, J. Comb. Optim. (ISSN: 1382-6905) (2008) 1573–2886. (Print) (Online)]. Combining the common technique used in the above mentioned reference, we can compute a minimum weight connected dominating set with approximation ratio 9 + ϵ , beating the previous best result of 10 + ϵ in the same work.

On the dominating set polytope

In this paper, we study the dominating set polytope in the class of graphs that decompose by one-node cutsets where the pieces are cycles. We describe some classes of facets and procedures to construct facets of the polytope in that class of graphs, and establish some structural properties. As a consequence we obtain a complete description of the polytope by a system of inequalities when the graph is a cycle. We also show that the separation problem related to that system can be solved in polynomial time. This yields a polynomial time cutting plane algorithm for the minimum weight dominating set problem in that case. We further discuss the applications for the class of cactus graphs.

Distributed algorithms for weighted problems in sparse graphs

We study distributed algorithms for three graph-theoretic problems in weighted trees and weighted planar graphs. For trees, we present an efficient deterministic distributed algorithm which finds an almost exact approximation of a maximum-weight matching. In addition, in the case of trees, we show how to approximately solve the minimum-weight dominating set problem. For planar graphs, we present an almost exact approximation for the maximum-weight independent set problem.

The Minimum Weight Dominating Set Problem for Permutation Graphs Is in NC

In this paper, we show that the problem of finding a minimum weight dominating set in a permutation graph, where a positive weight is assigned to each vertex, is in NC by presenting an O(log n) parallel algorithm with polynomially many processors on the CRCW model.