{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:44Z","timestamp":1753889924604,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T00:00:00Z","timestamp":1540944000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T00:00:00Z","timestamp":1540944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T00:00:00Z","timestamp":1540944000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100014013","name":"UK Research and Innovation","doi-asserted-by":"crossref","award":["EP\/L011018\/1"],"award-info":[{"award-number":["EP\/L011018\/1"]}],"id":[{"id":"10.13039\/100014013","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Strategy improvement is a widely-used and well-studied class of algorithms for solving graph-based infinite games. These algorithms are parameterized by a switching rule, and one of the most natural rules is &amp;quot;all switches&amp;quot; which switches as many edges as possible in each iteration. Continuing a recent line of work, we study all-switches strategy improvement from the perspective of computational complexity. We consider two natural decision problems, both of which have as input a game $G$, a starting strategy $s$, and an edge $e$. The problems are: 1.) The edge switch problem, namely, is the edge $e$ ever switched by all-switches strategy improvement when it is started from $s$ on game $G$? 2.) The optimal strategy problem, namely, is the edge $e$ used in the final strategy that is found by strategy improvement when it is started from $s$ on game $G$? We show $\\mathtt{PSPACE}$-completeness of the edge switch problem and optimal strategy problem for the following settings: Parity games with the discrete strategy improvement algorithm of V\\&amp;quot;oge and Jurdzi\\'nski; mean-payoff games with the gain-bias algorithm [14,37]; and discounted-payoff games and simple stochastic games with their standard strategy improvement algorithms. We also show $\\mathtt{PSPACE}$-completeness of an analogous problem to edge switch for the bottom-antipodal algorithm for finding the sink of an Acyclic Unique Sink Orientation on a cube.<\/jats:p>","DOI":"10.23638\/lmcs-14(4:9)2018","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:33:32Z","timestamp":1743701612000},"source":"Crossref","is-referenced-by-count":0,"title":["The Complexity of All-switches Strategy Improvement"],"prefix":"10.23638","volume":"Volume 14, Issue 4","author":[{"given":"John","family":"Fearnley","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1262-7831","authenticated-orcid":false,"given":"Rahul","family":"Savani","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2018,10,31]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1507.04500v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1507.04500v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:33:32Z","timestamp":1743701612000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/3794"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,31]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-14(4:9)2018","relation":{"has-preprint":[{"id-type":"arxiv","id":"1507.04500v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1507.04500v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1507.04500","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1507.04500","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2018,10,31]]},"article-number":"3794"}}