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)


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.


Directed Graph Hamiltonian Cycle Partial Cover Perfectness Condition Adjacency Graph 
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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

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

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