Efficient maximum matching algorithms for trapezoid graphs

Abstract

Trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. Many NPhard problems can be solved in polynomial time if they are restricted on trapezoid graphs. A matching in a graph is a set of pairwise disjoint edges, and a maximum matching is a matching of maximum size. In this paper, we first propose an O(n(log n)3 ) algorithm for finding a maximum matching in trapezoid graphs, then improve the complexity to O(n(log n)2 ). Finally, we generalize this algorithm to a larger graph class, namely k-trapezoid graphs. To the best of our knowledge, these are the first efficient maximum matching algorithms for trapezoid graphs.

Efficient algorithms for maximum induced matching problem in permutation and trapezoid graphs

“…Denote n and m as the number of vertices and edges in a graph, respectively. Do et al [19] introduced an efficient algorithm to find a maximum matching in trapezoid graphs in O(n(log n) 2 ). On the other hand, Rhee et al [20] proposed an O(n log log n) algorithm for such problems in permutation graphs.…”

An efficient implementation of the Gale and Shapley “propose-and-reject” algorithm

“…When every node is involved in a matching, then this matching is called perfect matching. The need to efficiently compute matchings arises often in a wide range of popular algorithmic problems (see, e.g., [4,16,19]) which include scheduling, bipartite matching, independent set, competitive facility location and have also been been recently addressed in more theoretical contexts (see, e.g., [2,5]).…”