{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2405.02479"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"KrCh"}],"ec_funded":1,"language":[{"iso":"eng"}],"acknowledgement":"This research was partially supported by the ERC CoG 863818 (ForM-SMArt) grant.\r\n","author":[{"first_name":"Ali","full_name":"Asadi, Ali","last_name":"Asadi","id":"02d96aae-000e-11ec-b801-cadd0a5eefbb"},{"last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","first_name":"Krishnendu"},{"full_name":"Saona Urmeneta, Raimundo J","first_name":"Raimundo J","orcid":"0000-0001-5103-038X","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","last_name":"Saona Urmeneta"},{"id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","last_name":"Svoboda","first_name":"Jakub","orcid":"0000-0002-1419-3267","full_name":"Svoboda, Jakub"}],"day":"20","year":"2024","date_published":"2024-05-20T00:00:00Z","article_processing_charge":"No","article_number":"2405.02479","date_updated":"2024-06-03T08:13:19Z","publication":"arXiv","status":"public","date_created":"2024-06-03T07:43:15Z","abstract":[{"lang":"eng","text":"Turn-based discounted-sum games are two-player zero-sum games played on\r\nfinite directed graphs. The vertices of the graph are partitioned between\r\nplayer 1 and player 2. Plays are infinite walks on the graph where the next\r\nvertex is decided by a player that owns the current vertex. Each edge is\r\nassigned an integer weight and the payoff of a play is the discounted-sum of\r\nthe weights of the play. The goal of player 1 is to maximize the discounted-sum\r\npayoff against the adversarial player 2. These games lie in NP and coNP and are\r\namong the rare combinatorial problems that belong to this complexity class and\r\nthe existence of a polynomial-time algorithm is a major open question. Since\r\nbreaking the general exponential barrier has been a challenging problem, faster\r\nparameterized algorithms have been considered. If the discount factor is\r\nexpressed in unary, then discounted-sum games can be solved in polynomial time.\r\nHowever, if the discount factor is arbitrary (or expressed in binary), but the\r\nweights are in unary, none of the existing approaches yield a sub-exponential\r\nbound. Our main result is a new analysis technique for a classical algorithm\r\n(namely, the strategy iteration algorithm) that present a new runtime bound\r\nwhich is $n^{O ( W^{1/4} \\sqrt{n} )}$, for game graphs with $n$ vertices and\r\nmaximum absolute weight of at most $W$. In particular, our result yields a\r\ndeterministic sub-exponential bound for games with weights that are constant or\r\nrepresented in unary."}],"oa_version":"Preprint","type":"preprint","citation":{"chicago":"Asadi, Ali, Krishnendu Chatterjee, Raimundo J Saona Urmeneta, and Jakub Svoboda. “Deterministic Sub-Exponential Algorithm for Discounted-Sum Games with Unary Weights.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2405.02479\">https://doi.org/10.48550/arXiv.2405.02479</a>.","ieee":"A. Asadi, K. Chatterjee, R. J. Saona Urmeneta, and J. Svoboda, “Deterministic sub-exponential algorithm for discounted-sum games with unary weights,” <i>arXiv</i>. .","mla":"Asadi, Ali, et al. “Deterministic Sub-Exponential Algorithm for Discounted-Sum Games with Unary Weights.” <i>ArXiv</i>, 2405.02479, doi:<a href=\"https://doi.org/10.48550/arXiv.2405.02479\">10.48550/arXiv.2405.02479</a>.","ista":"Asadi A, Chatterjee K, Saona Urmeneta RJ, Svoboda J. Deterministic sub-exponential algorithm for discounted-sum games with unary weights. arXiv, 2405.02479.","ama":"Asadi A, Chatterjee K, Saona Urmeneta RJ, Svoboda J. Deterministic sub-exponential algorithm for discounted-sum games with unary weights. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2405.02479\">10.48550/arXiv.2405.02479</a>","apa":"Asadi, A., Chatterjee, K., Saona Urmeneta, R. J., &#38; Svoboda, J. (n.d.). Deterministic sub-exponential algorithm for discounted-sum games with unary weights. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2405.02479\">https://doi.org/10.48550/arXiv.2405.02479</a>","short":"A. Asadi, K. Chatterjee, R.J. Saona Urmeneta, J. Svoboda, ArXiv (n.d.)."},"doi":"10.48550/arXiv.2405.02479","_id":"17098","month":"05","title":"Deterministic sub-exponential algorithm for discounted-sum games with unary weights","external_id":{"arxiv":["2405.02479"]},"publication_status":"submitted","oa":1,"project":[{"call_identifier":"H2020","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}]}