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On the Complexity of Optimal Matching Reconfiguration

  • Manoj Gupta
  • Hitesh Kumar
  • Neeldhara MisraEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11376)

Abstract

We consider the problem of matching reconfiguration, where we are given two matchings \(M_s\) and \(M_t\) in a graph G and the goal is to determine if there exists a sequence of matchings \(M_0, M_1, \ldots , M_\ell \), such that \(M_0 = M_s\), all consecutive matchings differ by exactly two edges (specifically, any matching is obtained from the previous one by the addition and deletion of one edge), and \(M_\ell = M_t\). It is known that the existence of such a sequence can be determined in polynomial time [5].

We extend the study of reconfiguring matchings to account for the length of the reconfiguration sequence. We show that checking if we can reconfigure \(M_s\) to \(M_t\) in at most \(\ell \) steps is NP-hard, even when the graph is unweighted, bipartite, and the maximum degree is four, and the matchings \(M_s\) and \(M_t\) are maximum matchings. We propose two simple algorithmic approaches, one of which improves on the brute-force running time while the other is a SAT formulation that we expect will be useful in practice.

Keywords

Graph theory Reconfiguration Matchings NP-hardness 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Indian Institute of Technology, GandhinagarGandhinagarIndia
  2. 2.NISER BhubaneswarBhubaneswarIndia

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