Circuit Complexity of Properties of Graphs with Constant Planar Cutwidth

  • Kristoffer Arnsfelt Hansen
  • Balagopal Komarath
  • Jayalal Sarma
  • Sven Skyum
  • Navid Talebanfard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8635)

Abstract

We study the complexity of several of the classical graph decision problems in the setting of bounded cutwidth and how imposing planarity affects the complexity. We show that for 2-coloring, for bipartite perfect matching, and for several variants of disjoint paths, the straightforward NC 1 upper bound may be improved to AC 0[2], ACC 0, and AC 0 respectively for bounded planar cutwidth graphs. We obtain our upper bounds using the characterization of these circuit classes in tems of finite monoids due to Barrington and Thérien. On the other hand we show that 3-coloring and Hamilton cycle remain hard for NC 1 under projection reductions, analogous to the NP-completeness for general planar graphs. We also show that 2-coloring and (non-bipartite) perfect matching are hard under projection reductions for certain subclasses of AC 0[2]. In particular this shows that our bounds for 2-coloring are quite close.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Kristoffer Arnsfelt Hansen
    • 1
  • Balagopal Komarath
    • 2
  • Jayalal Sarma
    • 2
  • Sven Skyum
    • 1
  • Navid Talebanfard
    • 1
  1. 1.Aarhus UniversityDenmark
  2. 2.IIT MadrasChennaiIndia

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