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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 1988: Graph-Theoretic Concepts in Computer Science pp 1–10Cite as

NC-algorithms for graphs with small treewidth

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 344))

Abstract

In this paper we give a parallel algorithm for recognizing graphs with treewidth ≤ k, for constant k, and building the corresponding tree-decomposition, that uses O(log n) time and O(n 3k+4) processors on a CRCW PRAM. Also, we give a parallel algorithm that transforms a given tree-decomposition of a graph G with treewidth k to another tree-decomposition of G with treewidth ≤ 3k+2, such that the tree in this tree-decomposition is binary and has logarithmic depth. The algorithm uses a linear number of processors and O(log n) time. Many NP-complete graph problems are known to be solvable in polynomial time, when restricted to graphs with treewidth ≤ k, k constant. From the results in this paper, it follows that most of these problems are also in NC, when restricted to graphs with treewidth bounded by a constant.

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Authors and Affiliations

  1. Department of Computer Science, University of Utrecht, P.O.Box 80.012, 3508 TA, Utrecht, the Netherlands

    Hans L. Bodlaender

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  1. Hans L. Bodlaender
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J. van Leeuwen

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© 1989 Springer-Verlag Berlin Heidelberg

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Bodlaender, H.L. (1989). NC-algorithms for graphs with small treewidth. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1988. Lecture Notes in Computer Science, vol 344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50728-0_32

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  • DOI: https://doi.org/10.1007/3-540-50728-0_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50728-4

  • Online ISBN: 978-3-540-46076-3

  • eBook Packages: Springer Book Archive

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