Journal Article10.1007/S11590-011-0351-X
Integer programming formulations for the minimum weighted maximal matching problem
Z. Caner Taşkın,Tınaz Ekim +1 more
14
TL;DR: This paper develops integer programming formulations for the minimum weighted maximal matching problem and analyzes their efficacy on randomly generated graphs and compares solutions found by a greedy approximation algorithm against optimal solutions.
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Abstract: Given an undirected graph, the problem of finding a maximal matching that has minimum total weight is NP-hard. This problem has been studied extensively from a graph theoretical point of view. Most of the existing literature considers the problem in some restricted classes of graphs and give polynomial time exact or approximation algorithms. On the contrary, we consider the problem on general graphs and approach it from an optimization point of view. In this paper, we develop integer programming formulations for the minimum weighted maximal matching problem and analyze their efficacy on randomly generated graphs. We also compare solutions found by a greedy approximation algorithm, which is based on the literature, against optimal solutions. Our results show that our integer programming formulations are able to solve medium size instances to optimality and suggest further research for improvement.
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Citations
Decomposition algorithms for solving the minimum weight maximal matching problem
TL;DR: This article develops integer programming (IP) formulations for the problem and devise a decomposition algorithm, which is based on a combination of IP techniques and combinatorial matching algorithms, and shows that this approach significantly improves the solvability of the problem compared to the underlying IP formulation.
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Maximal matching polytope in trees
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Bounding and approximating minimum maximal matchings in regular graphs
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Improved approximation bounds for edge dominating set in dense graphs
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2
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Mihalis Yannakakis,Fanica Gavril +1 more
TL;DR: In this article, it was shown that the edge dominating set problem for graphs is $NP$-complete even when restricted to planar or bipartite graphs of maximum degree 3.
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Hanif D. Sherali,J. Cole Smith +1 more
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