TY - GEN
T1 - Improved Bounds for Strategy Improvement Algorithms for Energy Games
AU - Dorfman, Dani
AU - Kaplan, Haim
AU - Zwick, Uri
N1 - Publisher Copyright:
© Dani Dorfman, Haim Kaplan, and Uri Zwick.
PY - 2026/8/25
Y1 - 2026/8/25
N2 - 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(n2n) 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 = 2n 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].
AB - 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(n2n) 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 = 2n 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].
KW - Energy Games
KW - Graph Games
KW - Strategy improvement
UR - https://www.scopus.com/pages/publications/105048953247
U2 - 10.4230/LIPIcs.ESA.2026.140
DO - 10.4230/LIPIcs.ESA.2026.140
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AN - SCOPUS:105048953247
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 34th Annual European Symposium on Algorithms, ESA 2026
A2 - Bille, Philip
A2 - Pettie, Seth
A2 - Storand, Sabine
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 34th Annual European Symposium on Algorithms, ESA 2026
Y2 - 31 August 2026 through 4 September 2026
ER -