Faster Algorithms for Semi-Matching Problems

We consider the problem of finding semi-matching in bipartite graphs which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted case. For the weighted case, we give an O(nm log n)-time algorithm, where n is the number of vertices and m is the number of edges, by exploiting the geometric structure of the problem. This improves the classical O(n3 ) algorithms by Horn [Operations Research 1973] and Bruno, Coffman and Sethi [Communications of the ACM 1974]. For the unweighted case, the bound could be improved even further. We give a simple divideand-conquer algorithm which runs in O( nm log n) time, improving two previous O(nm)-time algorithms by Abraham [MSc thesis, University of Glasgow 2003] and Harvey, Ladner, Lov

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Jittat Fakcharoenphol, Bundit Laekhanukit, Danupon Nanongkai
• Keywords: -time Algorithm, Algorithm, CORR 2010, Education, Simple Divideand-conquer Algorithm