Computing maximum non-crossing matching in convex bipartite graphs

Authors:
Danny Z. Chen;Xiaomin Liu;Haitao Wang
Affiliations:
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN;Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN;Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN
Venue:
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Year:
2012

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Abstract

We consider computing a maximum non-crossing matching in convex bipartite graphs. For a convex bipartite graph of n vertices and m edges, we present an O (n logn ) time algorithm for finding a maximum non-crossing matching in the graph. The previous best algorithm for this problem takes O (m +n logn ) time. Since m =Θ(n 2) in the worst case, our result improves the previous solution for large m .