On the stable b-matching problem in multigraphs

Authors:
Viera Borbel'ová;Katarína Cechlárová
Affiliations:
Faculty of Science, Institute of Mathematics, P.J. Šafárik University, Jesenná 5, 041 54 Košice, Slovakia;Faculty of Science, Institute of Mathematics, P.J. Šafárik University, Jesenná 5, 041 54 Košice, Slovakia
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

This paper deals with the stable b-matching problem in multigraphs, called the stable multiple activities problem, SMA for short. In an SMA instance a multigraph G=(V,E), capacity b(v) and a linear order @?"v on the set of edges incident to v, for each vertex v@?V are given. A stable b-matching is sought, i.e. a set of edges M such that each vertex v is incident with at most b(v) edges and for each edge e@?M a vertex v incident with e and b(v) distinct edges f"1,...,f"b"("v") incident to v exist in M, all of them @?"v-smaller than e. We show how to decrease the computational complexity of the SMA algorithm to run in O(|E|) time and derive some properties of stable b-matchings.