Approximation algorithms for the b-edge dominating set problem and its related problems

  • Authors:

  • Takuro Fukunaga;Hiroshi Nagamochi

  • Affiliations:

  • Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University

  • Venue:
  • COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
  • Year:
  • 2005

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Abstract

The edge dominating set problem is one of the fundamental covering problems in the field of combinatorial optimization. In this paper, we consider the b-edge dominating set problem, a generalized version of the edge dominating set problem. In this version, we are given a simple undirected graph G=(V,E) and a demand vector $b \in \mathbb{Z}_+^E$. A set F of edges in G is called a b-edge dominating set if each edge e ∈ E is adjacent to at least b(e) edges in F, where we allow F to contain multiple copies of edges in E. Given a cost vector $w \in \mathbb{Q}_+^E$, the problem asks to find a minimum cost of a b-edge dominating set. We first show that there is a $\frac{8}{3}$-approximation algorithm for this problem. We then consider approximation algorithms for other related problems.