The β-assignment problems

Chang, GJ

doi:10.1016/S0377-2217(97)00008-8

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The β-assignment problems

1998-02-01

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Chang, GJ

Ho, PH

DOI：10.1016/S0377-2217(97)00008-8

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Abstract

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Suppose G = (S, T, E) is a bipartite graph, where (S,T) is a bipartition of the vertex set. A beta-assignment is an edge set X subset of or equal to E such that deg(X)(i) = 1 for all i is an element of S. The cardinality beta-assignment problem is to find a beta-assignment X which minimizes beta(X) = max(j is an element of)T deg(X)(j). Suppose we associate every edge with a weight which is a real number. The bottleneck beta-assignment problem is to find a beta-assignment X that minimizes beta(X) and maximizes the minimum edge weight on X. The weighted beta-assignment problem is to find a beta-assignment X that minimizes beta(X) and maximizes the total weights of edges in X. This paper presents O(/SJ//E/)-time algorithms for the cardinality and the bottleneck beta-assignment problems and an O(/S/(2)/T/ + /S//T/(2))-time algorithm for the weighted beta-assignment problem. (C) 1998 Elsevier Science B.V.

Keywords:

assignment

bottleneck

augmenting path

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