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Latin American Symposium on Theoretical Informatics

LATIN 2002: LATIN 2002: Theoretical Informatics pp 613–627Cite as

Improved Tree Decomposition Based Algorithms for Domination-like Problems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2286))

Abstract

We present an improved dynamic programming strategy for dominating set and related problems on graphs that are given together with a tree decomposition of width k. We obtain an O(4k n) algorithm for dominating set, where n is the number of nodes of the tree decomposition. This result improves the previously best known algorithm of Telle and Proskurowski running in time O(9k n). The key to our result is an argument on a certain “monotonicity” in the table updating process during dynamic programming.

Moreover, various other domination-like problems as discussed by Telle and Proskurowski are treated with our technique. We gain improvements on the base of the exponential term in the running time ranging between 55% and 68% in most of these cases. These results mean significant breakthroughs concerning practical implementations.

Supported by the Deutsche Forschungsgemeinschaft (DFG), research project PEAL (Parameterized complexity and Exact ALgorithms), NI 369/1-1.

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Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076, Tübingen, Fed. Rep. of Germany

    Jochen Alber & Rolf Niedermeier

Authors
  1. Jochen Alber
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  2. Rolf Niedermeier
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Editor information

Editors and Affiliations

  1. Compaq Cambridge Research Laboratory, One Cambridge Center, 02142-1612, Cambridge, MA, USA

    Sergio Rajsbaum

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Alber, J., Niedermeier, R. (2002). Improved Tree Decomposition Based Algorithms for Domination-like Problems. In: Rajsbaum, S. (eds) LATIN 2002: Theoretical Informatics. LATIN 2002. Lecture Notes in Computer Science, vol 2286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45995-2_52

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  • DOI: https://doi.org/10.1007/3-540-45995-2_52

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43400-9

  • Online ISBN: 978-3-540-45995-8

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