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Planarity, Determinants, Permanents, and (Unique) Matchings

  • Samir Datta
  • Raghav Kulkarni
  • Nutan Limaye
  • Meena Mahajan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4649)

Abstract

We explore the restrictiveness of planarity on the complexity of computing the determinant and the permanent, and show that both problems remain as hard as in the general case, i.e. GapL and #P complete. On the other hand, both bipartite planarity and bimodal planarity bring the complexity of permanents down (but no further) to that of determinants. The permanent or the determinant modulo 2 is complete for ⊕L, and we show that parity of paths in a layered grid graph (which is bimodal planar) is also complete for this class. We also relate the complexity of grid graph reachability to that of testing existence/uniqueness of a perfect matching in a planar bipartite graph.

Keywords

Bipartite Graph Planar Graph Perfect Match Adjacency Matrix Directed Acyclic 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 2007

Authors and Affiliations

  • Samir Datta
    • 1
  • Raghav Kulkarni
    • 2
  • Nutan Limaye
    • 3
  • Meena Mahajan
    • 3
  1. 1.Chennai Mathematical Institute, Siruseri, Chennai 603 103India
  2. 2.Dept. of Computer Science, Univ. of ChicagoU.S.A.
  3. 3.The Institute of Mathematical Sciences, Chennai 600 113India

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