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Measure and Conquer: Domination – A Case Study

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Automata, Languages and Programming (ICALP 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3580))

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Abstract

Davis-Putnam-style exponential-time backtracking algorithms are the most common algorithms used for finding exact solutions of NP-hard problems. The analysis of such recursive algorithms is based on the bounded search tree technique: a measure of the size of the subproblems is defined; this measure is used to lower bound the progress made by the algorithm at each branching step.

For the last 30 years the research on exact algorithms has been mainly focused on the design of more and more sophisticated algorithms. However, measures used in the analysis of backtracking algorithms are usually very simple. In this paper we stress that a more careful choice of the measure can lead to significantly better worst case time analysis.

As an example, we consider the minimum dominating set problem. The currently fastest algorithm for this problem has running time O(20.850n) on n-nodes graphs. By measuring the progress of the (same) algorithm in a different way, we refine the time bound to O(20.598 n). A good choice of the measure can provide such a (surprisingly big) improvement; this suggests that the running time of many other exponential-time recursive algorithms is largely overestimated because of a “bad” choice of the measure.

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    Fedor V. Fomin

  2. Dipartimento di Informatica, Università di Roma “La Sapienza”, Via Salaria 113, 00198, Roma, Italy

    Fabrizio Grandoni

  3. LITA, Université de Metz, 57045, Metz Cedex 01, France

    Dieter Kratsch

Authors
  1. Fedor V. Fomin
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  2. Fabrizio Grandoni
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  3. Dieter Kratsch
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Editor information

Editors and Affiliations

  1. CITI / Departamento de Informática, Universidade Nova de Lisboa, Portugal

    Luís Caires

  2. Dipartimento di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Roma, Italy

    Giuseppe F. Italiano

  3. Departamento de Informatica, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Luís Monteiro

  4. Ecole Polytechnique, Rue de Saclay, 91128, Palaiseau Cedex, France

    Catuscia Palamidessi

  5. Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, NY 10027, New York, USA

    Moti Yung

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© 2005 Springer-Verlag Berlin Heidelberg

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Fomin, F.V., Grandoni, F., Kratsch, D. (2005). Measure and Conquer: Domination – A Case Study. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_16

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  • DOI: https://doi.org/10.1007/11523468_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27580-0

  • Online ISBN: 978-3-540-31691-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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