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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 1999: Graph-Theoretic Concepts in Computer Science pp 110–121Cite as

NLC2-Decomposition in Polynomial Time

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1665))

Abstract

NLCk is a family of algebras on vertex-labeled graphs introduced by Wanke. An NLC-decomposition of a graph is a derivation of this graph from single vertices using the operations in question. The width of the decomposition is the number of labels used, and the NLC-width of the graph is the smallest width among its NLC-decompositions. Many difficult graph problems can be solved efficiently with dynamic programming if an NLC-decomposition of low width is given for the input graph. It is unknown though whether arbitrary graphs of NLC-width at most k can be decomposed with k labels in polynomial time. So far this has been possible only for k = 1, which corresponds to cographs. In this paper, an algorithm is presented that works for k = 2. It runs in O(n 4 log n) time and uses O(n 2) space. Related concepts: clique-decomposition, cliquewidth.

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Author information

Authors and Affiliations

  1. Department of Numerical Analysis and Computing Science, Royal Institute of Technology, SE-100 44, Stockholm, Sweden

    Öjvind Johansson

Authors
  1. Öjvind Johansson
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Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science ETH Zürich ETH Zentrum, 8092, Zürich, Switzerland

    Peter Widmayer , Gabriele Neyer  & Stephan Eidenbenz ,  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Johansson, Ö. (1999). NLC2-Decomposition in Polynomial Time. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_12

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  • DOI: https://doi.org/10.1007/3-540-46784-X_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66731-5

  • Online ISBN: 978-3-540-46784-7

  • eBook Packages: Springer Book Archive

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