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An Extended Tree-Width Notion for Directed Graphs Related to the Computation of Permanents

  • Klaus Meer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6651)

Abstract

It is well known that permanents of matrices of bounded tree-width are efficiently computable. Here, the tree-width of a square matrix M = (m ij ) with entries from a field \(\mathbb{K}\) is the tree-width of the underlying graph G M having an edge (i,j) if and only if the entry m ij  ≠ 0. Though G M is directed this does not influence the tree-width definition. Thus, it does not reflect the lacking symmetry when m ij  ≠ 0 but m ji  = 0. The latter however might have impact on the computation of the permanent. In this paper we introduce and study an extended notion of tree-width called triangular tree-width. We give examples where the latter parameter is bounded whereas the former is not. As main result we show that permanents of matrices of bounded triangular tree-width are efficiently computable. This result holds as well for the Hamiltonian Cycle problem.

Keywords

Directed Graph Hamiltonian Cycle Partial Cover Perfectness Condition Adjacency 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 2011

Authors and Affiliations

  • Klaus Meer
    • 1
  1. 1.Lehrstuhl Theoretische InformatikBTU CottbusCottbusGermany

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