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Planarity, Determinants, Permanents, and (Unique) Matchings

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Book cover Computer Science – Theory and Applications (CSR 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4649))

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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.

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Authors and Affiliations

  1. Chennai Mathematical Institute, Siruseri, Chennai 603 103, India

    Samir Datta

  2. Dept. of Computer Science, Univ. of Chicago, U.S.A.

    Raghav Kulkarni

  3. The Institute of Mathematical Sciences, Chennai 600 113, India

    Nutan Limaye & Meena Mahajan

Authors
  1. Samir Datta
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  2. Raghav Kulkarni
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  3. Nutan Limaye
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  4. Meena Mahajan
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Volker Diekert Mikhail V. Volkov Andrei Voronkov

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Datta, S., Kulkarni, R., Limaye, N., Mahajan, M. (2007). Planarity, Determinants, Permanents, and (Unique) Matchings. In: Diekert, V., Volkov, M.V., Voronkov, A. (eds) Computer Science – Theory and Applications. CSR 2007. Lecture Notes in Computer Science, vol 4649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74510-5_14

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  • DOI: https://doi.org/10.1007/978-3-540-74510-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74509-9

  • Online ISBN: 978-3-540-74510-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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