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On the Enumeration and Counting of Minimal Dominating sets in Interval and Permutation Graphs

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Algorithms and Computation (ISAAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8283))

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Abstract

We reduce (in polynomial time) the enumeration of minimal dominating sets in interval and permutation graphs to the enumeration of paths in directed acyclic graphs(DAGs). As a consequence, we can enumerate with linear delay, after a polynomial time pre-processing, minimal dominating sets in interval and permutation graphs. We can also count them in polynomial time. This improves considerably upon previously known results on interval graphs, and up to our knowledge no output polynomial time algorithm for the enumeration of minimal dominating sets and their counting were known for permutation graphs.

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Author information

Authors and Affiliations

  1. LIMOS, CNRS, Clermont-Université, Université Blaise Pascal, France

    Mamadou Moustapha Kanté, Vincent Limouzy, Arnaud Mary & Lhouari Nourine

  2. National Institute of Informatics, Japan

    Takeaki Uno

Authors
  1. Mamadou Moustapha Kanté
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  2. Vincent Limouzy
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  3. Arnaud Mary
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  4. Lhouari Nourine
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  5. Takeaki Uno
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Chinese University of Hong Kong, Shatin, 100084, Hong Kong, China

    Leizhen Cai

  2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Clear Water Bay, 100044, Hong Kong, China

    Siu-Wing Cheng

  3. Department of Computer Science, University of Hong Kong, Porfkulam, 100084, Hong Kong, China

    Tak-Wah Lam

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© 2013 Springer-Verlag Berlin Heidelberg

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Kanté, M.M., Limouzy, V., Mary, A., Nourine, L., Uno, T. (2013). On the Enumeration and Counting of Minimal Dominating sets in Interval and Permutation Graphs. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_32

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  • DOI: https://doi.org/10.1007/978-3-642-45030-3_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45029-7

  • Online ISBN: 978-3-642-45030-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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