{"type":"journal_article","volume":70,"date_updated":"2023-09-05T14:09:29Z","abstract":[{"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. The existence of polynomial-time algorithms has been a major open problem for decades and apart from pseudopolynomial algorithms there is no algorithm that solves any non-trivial subclass in polynomial time. In 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 worst-case instances on which 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 the graph structure does not necessarily help.","lang":"eng"}],"publication":"Algorithmica","publication_status":"published","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"10905"}]},"author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H"},{"last_name":"Krinninger","full_name":"Krinninger, Sebastian","first_name":"Sebastian"},{"full_name":"Nanongkai, Danupon","first_name":"Danupon","last_name":"Nanongkai"}],"doi":"10.1007/s00453-013-9843-7","_id":"535","date_created":"2018-12-11T11:47:01Z","month":"11","citation":{"apa":"Chatterjee, K., Henzinger, M. H., Krinninger, S., &#38; Nanongkai, D. (2014). Polynomial-time algorithms for energy games with special weight structures. <i>Algorithmica</i>. Springer. <a href=\"https://doi.org/10.1007/s00453-013-9843-7\">https://doi.org/10.1007/s00453-013-9843-7</a>","ista":"Chatterjee K, Henzinger MH, Krinninger S, Nanongkai D. 2014. Polynomial-time algorithms for energy games with special weight structures. Algorithmica. 70(3), 457–492.","chicago":"Chatterjee, Krishnendu, Monika H Henzinger, Sebastian Krinninger, and Danupon Nanongkai. “Polynomial-Time Algorithms for Energy Games with Special Weight Structures.” <i>Algorithmica</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s00453-013-9843-7\">https://doi.org/10.1007/s00453-013-9843-7</a>.","ieee":"K. Chatterjee, M. H. Henzinger, S. Krinninger, and D. Nanongkai, “Polynomial-time algorithms for energy games with special weight structures,” <i>Algorithmica</i>, vol. 70, no. 3. Springer, pp. 457–492, 2014.","ama":"Chatterjee K, Henzinger MH, Krinninger S, Nanongkai D. Polynomial-time algorithms for energy games with special weight structures. <i>Algorithmica</i>. 2014;70(3):457-492. doi:<a href=\"https://doi.org/10.1007/s00453-013-9843-7\">10.1007/s00453-013-9843-7</a>","mla":"Chatterjee, Krishnendu, et al. “Polynomial-Time Algorithms for Energy Games with Special Weight Structures.” <i>Algorithmica</i>, vol. 70, no. 3, Springer, 2014, pp. 457–92, doi:<a href=\"https://doi.org/10.1007/s00453-013-9843-7\">10.1007/s00453-013-9843-7</a>.","short":"K. Chatterjee, M.H. Henzinger, S. Krinninger, D. Nanongkai, Algorithmica 70 (2014) 457–492."},"article_processing_charge":"No","department":[{"_id":"KrCh"}],"oa":1,"user_id":"72615eeb-f1f3-11ec-aa25-d4573ddc34fd","external_id":{"arxiv":["1604.08234"]},"page":"457 - 492","status":"public","project":[{"name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF","grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"name":"Game Theory","call_identifier":"FWF","grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425"},{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7"},{"_id":"2587B514-B435-11E9-9278-68D0E5697425","name":"Microsoft Research Faculty Fellowship"}],"language":[{"iso":"eng"}],"intvolume":"        70","publist_id":"7282","oa_version":"Preprint","issue":"3","title":"Polynomial-time algorithms for energy games with special weight structures","quality_controlled":"1","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1604.08234","open_access":"1"}],"date_published":"2014-11-01T00:00:00Z","day":"01","ec_funded":1,"year":"2014","publisher":"Springer","article_type":"original"}