Simultaneous Matchings
نویسندگان
چکیده
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 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 the 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(2poly(k, |X ∪ D|)) time.
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