Browsing by Author "Ho, PH"

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The beta-assignment problem in general graphs
(1997-08-01)
Chang, GJ
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Ho, PH
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應用數學系
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Department of Applied Mathematics
We study a variation of the assignment problem in operations research and formulate it in terms of graphs as follows. Suppose G=(V,E) is a graph and U a subset of V.! A beta-assignment of G with respect to U is an edge set X such that deg(X)(nu)=1 for all vertices nu in U, where deg(X)(nu) is the degree of nu in the subgraph of G induced by the edge set X. The beta-assignment problem is to find a beta-assignment X such that beta(X)=max {deg(X)(nu):nu is an element of V-U} is minimum. The purpose of this paper is to give an O(n(3))-time algorithm for the beta-assignment problem in general graphs. As byproducts, we also obtain a duality theorem as well as a necessary and sufficient condition for the existence of a beta-assignment for a general graph. The latter result is a generalization of Tutte's theorem for the existence of a perfect matching of a general graph. (C) 1997 Elsevier Science Ltd.
The beta-assignment problems
(1998-02-01)
Chang, GJ
;
Ho, PH
;
應用數學系
;
Department of Applied Mathematics
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.