ISAAC 2005: Algorithms and Computation pp 106-115

# Simultaneous Matchings

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

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

## Keywords

Feasible Solution Bipartite Graph Constraint Programming Complete Bipartite Graph Maximal Subset
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## 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