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.
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References
Arkin, E.M., Halldórsson, M.M., Hassin, R.: Approximating the tree and tour cover of graph. Information Processing Letters 47, 275–282 (1993)
Carr, R., Fujito, T., Konjevod, G., Parekh, O.: A \(2\frac{1}{10}\)-approximation algorithm for a generalization of the weighted edge-dominating set problem. In: Paterson, M. (ed.) ESA 2000. LNCS, vol. 1879, pp. 132–142. Springer, Heidelberg (2000)
Chvátal, V.: A greedy heuristics for the set covering problem. Mathematics of Operations Research 4, 233–235 (1979)
Fujito, T., Nagamochi, H.: A 2-approximation algorithm for the minimum weight edge dominating set problem. Discrete Applied Mathmatics 118, 199–207 (2002)
Garey, M.R., Johnson, D.S.: Computers and Intractability; a Guide to the Theory of NP-completeness. W. H. Freeman & Co., New York (1979)
Harary, F.: Graph Theory. Addison-Wesley, Reading (1969)
Könemann, J., Konjevod, G., Parekh, O., Sinha, A.: Improved approximations for tour and tree covers. Algorithmica 38, 441–449 (2004)
Lovász, L.: On the ratio of optimal integral and fractional covers. Discrete Mathematics 13, 383–390 (1975)
Murty, K.G., Perin, C.: A 1-matching blossom-type algorithm for edge covering problems. Networks 12, 379–391 (1982)
Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Heidelberg (2003)
Yannakakis, M., Gavril, F.: Edge dominating sets in graphs SIAM Journal on Applied Mathematics, vol. SIAM Journal on Applied Mathematics 38, 364–372 (1980)
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Fukunaga, T., Nagamochi, H. (2005). Approximation Algorithms for the b-Edge Dominating Set Problem and Its Related Problems. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_76
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DOI: https://doi.org/10.1007/11533719_76
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28061-3
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