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Fixed-Dimensional Energy Games are in Pseudo-Polynomial Time

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Automata, Languages, and Programming (ICALP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9135))

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Abstract

We generalise the hyperplane separation technique (Chatterjee and Velner, 2013) from multi-dimensional mean-payoff to energy games, and achieve an algorithm for solving the latter whose running time is exponential only in the dimension, but not in the number of vertices of the game graph. This answers an open question whether energy games with arbitrary initial credit can be solved in pseudo-polynomial time for fixed dimensions 3 or larger (Chaloupka, 2013). It also improves the complexity of solving multi-dimensional energy games with given initial credit from non-elementary (Brázdil, Jančar, and Kučera, 2010) to 2EXPTIME, thus establishing their 2EXPTIME-completeness.

Work funded in part by the ANR grant 11-BS02-001-01 ReacHard, the Leverhulme Trust Visiting Professorship VP1-2014-041, and the EPSRC grant EP/M011801/1.

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Author information

Authors and Affiliations

  1. DIMAP, Department of Computer Science, University of Warwick, Coventry, UK

    Marcin Jurdziński, Ranko Lazić & Sylvain Schmitz

  2. LSV, ENS Cachan & CNRS & INRIA, Cachan Cedex, France

    Sylvain Schmitz

Authors
  1. Marcin Jurdziński
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  2. Ranko Lazić
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  3. Sylvain Schmitz
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Corresponding author

Correspondence to Sylvain Schmitz .

Editor information

Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Kyoto University, Kyoto, Japan

    Kazuo Iwama

  3. The University of Tokyo, Tokyo, Japan

    Naoki Kobayashi

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Bettina Speckmann

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Jurdziński, M., Lazić, R., Schmitz, S. (2015). Fixed-Dimensional Energy Games are in Pseudo-Polynomial Time. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47666-6_21

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  • DOI: https://doi.org/10.1007/978-3-662-47666-6_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47665-9

  • Online ISBN: 978-3-662-47666-6

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