The minimum cost perfect matching problem with conflict pair constraints

Authors:
Temel ÖNcan;Ruonan Zhang;Abraham P. Punnen
Affiliations:
Endüstri Mühendisliği Bölümü, Galatasaray íniversitesi, Ortaköy, İstanbul, 34357, Türkiye;Department of Mathematics, Simon Fraser University Surrey, Central City, 250-13450 102nd AV, Surrey, British Columbia, Canada V3T 0A3;Department of Mathematics, Simon Fraser University Surrey, Central City, 250-13450 102nd AV, Surrey, British Columbia, Canada V3T 0A3
Venue:
Computers and Operations Research
Year:
2013

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Abstract

In this paper we address the minimum cost perfect matching problem with conflict pair constraints (MCPMPC). Given an undirected graph G with a cost associated with each edge and a conflict set of pairs of edges, the MCPMPC is to find a perfect matching with the lowest total cost such that no more than one edge is selected from each pair in the conflict set. MCPMPC is known to be strongly NP-hard. We present additional complexity results and identify new polynomially solvable cases for the general MCPMPC. Several heuristic algorithms and lower bounding schemes are presented. The proposed algorithms are tested on randomly generated instances. Encouraging experimental results are also reported.