{"author":[{"last_name":"Chatterjee","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H"},{"full_name":"Krinninger, Sebastian","first_name":"Sebastian","last_name":"Krinninger"},{"first_name":"Danupon","last_name":"Nanongkai","full_name":"Nanongkai, Danupon"}],"page":"301-312","oa_version":"Preprint","scopus_import":"1","_id":"10905","related_material":{"record":[{"relation":"later_version","status":"public","id":"535"}]},"conference":{"start_date":"2012-09-10","location":"Ljubljana, Slovenia","name":"ESA: European Symposium on Algorithms","end_date":"2012-09-12"},"alternative_title":["LNCS"],"language":[{"iso":"eng"}],"year":"2012","oa":1,"date_published":"2012-10-01T00:00:00Z","day":"01","date_created":"2022-03-21T08:01:45Z","external_id":{"arxiv":["1604.08234"]},"volume":7501,"quality_controlled":"1","intvolume":"      7501","title":"Polynomial-time algorithms for energy games with special weight structures","type":"conference","department":[{"_id":"KrCh"}],"month":"10","status":"public","project":[{"grant_number":"S11407","call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory"},{"name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425"},{"_id":"2587B514-B435-11E9-9278-68D0E5697425","name":"Microsoft Research Faculty Fellowship"}],"ec_funded":1,"publisher":"Springer","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_identifier":{"isbn":["9783642330896"],"eisbn":["9783642330902"],"eissn":["1611-3349"],"issn":["0302-9743"]},"abstract":[{"lang":"eng","text":"Energy games belong to a class of turn-based two-player infinite-duration games played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in NP ∩ co−NP, but are not known to be in P. While the existence of polynomial-time algorithms has been a major open problem for decades, there is no algorithm that solves any non-trivial subclass in polynomial time.\r\nIn this paper, we give several results based on the weight structures of the graph. First, we identify a notion of penalty and present a polynomial-time algorithm when the penalty is large. Our algorithm is the first polynomial-time algorithm on a large class of weighted graphs. It includes several counter examples that show that many previous algorithms, such as value iteration and random facet algorithms, require at least sub-exponential time. Our main technique is developing the first non-trivial approximation algorithm and showing how to convert it to an exact algorithm. Moreover, we show that in a practical case in verification where weights are clustered around a constant number of values, the energy game problem can be solved in polynomial time. We also show that the problem is still as hard as in general when the clique-width is bounded or the graph is strongly ergodic, suggesting that restricting graph structures need not help."}],"acknowledgement":"Supported by the Austrian Science Fund (FWF): P23499-N23, the Austrian Science Fund (FWF): S11407-N23 (RiSE), an ERC Start Grant (279307: Graph Games), and a Microsoft Faculty Fellows Award","doi":"10.1007/978-3-642-33090-2_27","article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1604.08234"}],"citation":{"apa":"Chatterjee, K., Henzinger, M. H., Krinninger, S., &#38; Nanongkai, D. (2012). Polynomial-time algorithms for energy games with special weight structures. In <i>Algorithms – ESA 2012</i> (Vol. 7501, pp. 301–312). Ljubljana, Slovenia: Springer. <a href=\"https://doi.org/10.1007/978-3-642-33090-2_27\">https://doi.org/10.1007/978-3-642-33090-2_27</a>","ieee":"K. Chatterjee, M. H. Henzinger, S. Krinninger, and D. Nanongkai, “Polynomial-time algorithms for energy games with special weight structures,” in <i>Algorithms – ESA 2012</i>, Ljubljana, Slovenia, 2012, vol. 7501, pp. 301–312.","ama":"Chatterjee K, Henzinger MH, Krinninger S, Nanongkai D. Polynomial-time algorithms for energy games with special weight structures. In: <i>Algorithms – ESA 2012</i>. Vol 7501. Springer; 2012:301-312. doi:<a href=\"https://doi.org/10.1007/978-3-642-33090-2_27\">10.1007/978-3-642-33090-2_27</a>","short":"K. Chatterjee, M.H. Henzinger, S. Krinninger, D. Nanongkai, in:, Algorithms – ESA 2012, Springer, 2012, pp. 301–312.","chicago":"Chatterjee, Krishnendu, Monika H Henzinger, Sebastian Krinninger, and Danupon Nanongkai. “Polynomial-Time Algorithms for Energy Games with Special Weight Structures.” In <i>Algorithms – ESA 2012</i>, 7501:301–12. Springer, 2012. <a href=\"https://doi.org/10.1007/978-3-642-33090-2_27\">https://doi.org/10.1007/978-3-642-33090-2_27</a>.","ista":"Chatterjee K, Henzinger MH, Krinninger S, Nanongkai D. 2012. Polynomial-time algorithms for energy games with special weight structures. Algorithms – ESA 2012. ESA: European Symposium on Algorithms, LNCS, vol. 7501, 301–312.","mla":"Chatterjee, Krishnendu, et al. “Polynomial-Time Algorithms for Energy Games with Special Weight Structures.” <i>Algorithms – ESA 2012</i>, vol. 7501, Springer, 2012, pp. 301–12, doi:<a href=\"https://doi.org/10.1007/978-3-642-33090-2_27\">10.1007/978-3-642-33090-2_27</a>."},"publication":"Algorithms – ESA 2012","publication_status":"published","date_updated":"2023-09-05T14:09:30Z"}