The Worst-Case Complexity of Symmetric Strategy Improvement

T. van Dijk, G. Loho, M.T. Maat

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)
13 Downloads (Pure)

Abstract

Symmetric strategy improvement is an algorithm introduced by Schewe et al. (ICALP 2015) that can be used to solve two-player games on directed graphs such as parity games and mean payoff games. In contrast to the usual well-known strategy improvement algorithm, it iterates over strategies of both players simultaneously. The symmetric version solves the known worst-case examples for strategy improvement quickly, however its worst-case complexity remained open. We present a class of worst-case examples for symmetric strategy improvement on which this symmetric version also takes exponentially many steps. Remarkably, our examples exhibit this behaviour for any choice of improvement rule, which is in contrast to classical strategy improvement where hard instances are usually hand-crafted for a specific improvement rule. We present a generalized version of symmetric strategy iteration depending less rigidly on the interplay of the strategies of both players. However, it turns out it has the same shortcomings.
Original languageEnglish
Title of host publication32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)
EditorsAniello Murano, Alexandra Silva
Pages24.1-24.19
ISBN (Electronic)9783959773102
DOIs
Publication statusPublished - 7 Feb 2024
Event32nd EACSL Annual Conference on Computer Science Logic, CSL 2024 - Naples, Italy
Duration: 19 Feb 202423 Feb 2024
Conference number: 32

Conference

Conference32nd EACSL Annual Conference on Computer Science Logic, CSL 2024
Abbreviated titleCSL 2024
Country/TerritoryItaly
CityNaples
Period19/02/2423/02/24

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