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arXiv · 1905.04853

Maximum Weighted Matching with Few Edge Crossings for 2-Layered Bipartite Graph

Kazuya Haraguchi·Kotaro Torii·Motomu Endo
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Abstract

Let c denote a non-negative constant. Suppose that we are given an edge-weighted bipartite graph G=(V,E) with its 2-layered drawing and a family X of intersecting edge pairs. We consider the problem of finding a maximum weighted matching M* such that each edge in M* intersects with at most c other edges in M*, and that all edge crossings in M* are contained in X. In the present paper, we propose polynomial-time algorithms for the cases of c=1 and 2. The time complexities of the algorithms are O((k+m)log n+n) for c=1 and O(k^3+k^2n+m(m+log n)) for c=2, respectively, where n=|V|, m=|E| and k=|X|.

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Kazuya Haraguchi, Kotaro Torii, Motomu Endo. 2019-05-13. Maximum Weighted Matching with Few Edge Crossings for 2-Layered Bipartite Graph. https://arxiv.org/abs/1905.04853

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