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Improved Bounds for Strategy Improvement Algorithms for Energy Games

Authors Dani Dorfman , Haim Kaplan , Uri Zwick

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LIPIcs.ESA.2026.140.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Graph Games
  • Energy Games
  • Strategy improvement

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Abstract

Strategy improvement is a natural and well-studied family of algorithms for solving various classes of stochastic and deterministic graph games. We present an improved upper bound of O(n 2ⁿ) on the number of iterations performed by the most natural, and most greedy, variant of the algorithm when applied to n-vertex Energy Games. We also obtain a similar upper bound of O(poly(n)⋅ 2ⁿ) on the expected number of iterations performed by Random-Edge, one of the most natural randomized variants of the algorithm. To the best of our knowledge, these are the first bounds for natural strategy-improvement algorithms on non-binary energy games that beat the trivial nⁿ = 2^{n log n} bound obtained by enumerating all strategies. The proof is based on a new adaptation of the layering technique of [Dorfman, Kaplan, Zwick, ICALP 2019].

Cite As Get BibTex

Dani Dorfman, Haim Kaplan, and Uri Zwick. Improved Bounds for Strategy Improvement Algorithms for Energy Games. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 140:1-140:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.140

Author Details

Dani Dorfman
  • Max Planck Institute for Informatics, Saarbrücken, Germany
Haim Kaplan
  • Tel Aviv University, Israel
Uri Zwick
  • Tel Aviv University, Israel

Funding

  • Kaplan, Haim: This work was supported in part by Israel Science Foundation grant no. 1156-23 and the Blavatnik Family Foundation.
  • Zwick, Uri: This work was supported in part by Israel Science Foundation grant no. 2854/20.

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