Simultaneous matchings

  • Authors:

  • Khaled Elbassioni;Irit Katriel;Martin Kutz;Meena Mahajan

  • Affiliations:

  • Max-Plank-Institut für Informatik, Saarbrücken, Germany;BRICS, University of Aarhus, Århus, Denmark;Max-Plank-Institut für Informatik, Saarbrücken, Germany;The Institute of Mathematical Sciences, Chennai, India

  • Venue:
  • ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
  • Year:
  • 2005

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Abstract

Given a bipartite graph $G = (X \dot{\cup} D,E \subseteq X \times D)$, an X-perfect matching is a matching in G that covers 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 $\mathcal{F} \subseteq 2^{X}$ of k subsets of X, find a subset M⊆E of the edges such that for each $C \in \mathcal{F}$, 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 2kpoly(k,|X ∪ D|) time.