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A New NC-Algorithm for Finding a Perfect Matching in d-Regular Bipartite Graphs When d Is Small

  • Raghav Kulkarni
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3998)

Abstract

The perfect matching problem for general graphs reduces to the same for regular graphs. Even finding an NC algorithm for the perfect matching problem in cubic (3-regular) or 4-regular graphs will suffice to solve the general problem (see [DK 92]). For regular bipartite graphs an NC algorithm is already known [LPV 81], while [SW 96] give an NC algorithm for cubic-bipartite graphs.

We present a new and conceptually simple parallel algorithm for finding a perfect matching in d-regular bipartite graphs. When d is small (polylogarithmic) our algorithm in fact runs in NC. In particular for cubic-bipartite graphs, our algorithm as well as its analysis become much simpler than the previously known algorithms for the same. Our techniques are completely different from theirs.

Interestingly, our algorithm is based on a method used by [MV 00] for finding a perfect matching in planar-bipartite graphs. So, it is remarkable that, circumventing the planarity, we could still make the same approach work for a non-planar subclass of biparitite graphs.

Keywords

Span Tree Bipartite Graph Interior Point Perfect Match Regular Graph 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Raghav Kulkarni
    • 1
  1. 1.The Department of Computer ScienceUniversity of ChicagoChicagoUSA

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