Maximum Weighted Matching With Few Edge Crossings For 2-Layered Bipartite Graph

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 chi subset of E x E 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 chi. 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) or O(k + n(2)) for c = 1 and O(k(3) + k(2)n + m(2) + min{m log n, n(2)}) for c = 2, respectively, where n = vertical bar V vertical bar, m = vertical bar E vertical bar and k = vertical bar chi vertical bar. (C) 2020 Elsevier B.V. All rights reserved.