Simultaneous Matchings

  • Khaled Elbassioni
  • Irit Katriel
  • Martin Kutz
  • Meena Mahajan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3827)


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 2 k poly(k,|XD|) time.


Feasible Solution Bipartite Graph Constraint Programming Complete Bipartite Graph Maximal Subset 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Khaled Elbassioni
    • 1
  • Irit Katriel
    • 2
  • Martin Kutz
    • 1
  • Meena Mahajan
    • 3
  1. 1.Max-Plank-Institut für InformatikSaarbrückenGermany
  2. 2.BRICSUniversity of AarhusÅrhusDenmark
  3. 3.The Institute of Mathematical SciencesChennaiIndia

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