The -Assignment Problems
نویسندگان
چکیده
Suppose G = (S; T; E) is a bipartite graph, where (S; T) is a bipartition of the vertex set. A-assignment is an edge set X E such that deg X (i) = 1 for all i 2 S. The cardinality-assignment problem is to nd a-assignment X which minimizes (X) = max j2T deg X (j). Suppose we associate every edge with a weight which is a real number. The bottleneck-assignment problem is to nd a-assignment X that minimizes (X) and maximizes the minimum edge weight on X. The weighted-assignment problem is to nd a-assignment X that minimizes (X) and maximizes the total weights of edges in X. This paper presents O(jSjjEj)-time algorithms for the cardinality and the bottleneck-assignment problems and an O(jSj 2 jTj + jSjjTj 2)-time algorithm for the weighted-assignment problem.
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