Simultaneous Matchings [chapter]

Khaled Elbassioni, Irit Katriel, Martin Kutz, Meena Mahajan
2005 Lecture Notes in Computer Science  
Given a bipartite graph G = (X ∪ D, E ⊆ X × D), an Xperfect matching is a matching in G that saturates every node in X. In this paper we study the following generalisation of the X-perfect matching problem, which has applications in constraint programming: Given a bipartite graph as above and a collection F ⊆ 2 X of k subsets of X, find a subset M ⊆ E of the edges such that for each C ∈ F, the edge set M ∩ (C × D) is a C-perfect matching in G (or report that no such set exists). We show that
more » ... decision problem is NP-complete and that the corresponding optimisation problem is in APX when k = O(1) and even APX-complete already for k = 2. On the positive side, we show that a 2/(k + 1)-approximation can be found in O(2 k poly(k, |X ∪ D|)) time.
doi:10.1007/11602613_12 fatcat:bp2pstjafjbkbgktmjs5txp4tm