{"type":"journal_article","date_updated":"2022-09-09T11:50:58Z","volume":547,"abstract":[{"lang":"eng","text":"We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that the algorithmic question is reducible to the problem of a logarithmic number of min-plus matrix multiplications of n×n-matrices, where n is the number of vertices of the graph. (2) Second, when the weights are nonnegative, we present the first (1+ε)-approximation algorithm for the problem and the running time of our algorithm is Õ(nωlog3(nW/ε)/ε),1 where O(nω) is the time required for the classic n×n-matrix multiplication and W is the maximum value of the weights. With an additional O(log(nW/ε)) factor in space a cycle with approximately optimal weight can be computed within the same time bound."}],"publication":"Theoretical Computer Science","publication_status":"published","_id":"1375","author":[{"last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","orcid":"0000-0002-4561-241X"},{"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","first_name":"Sebastian","full_name":"Krinninger, Sebastian"},{"last_name":"Loitzenbauer","first_name":"Veronika","full_name":"Loitzenbauer, Veronika"},{"last_name":"Raskin","full_name":"Raskin, Michael","first_name":"Michael"}],"doi":"10.1016/j.tcs.2014.06.031","month":"08","date_created":"2018-12-11T11:51:40Z","citation":{"chicago":"Chatterjee, Krishnendu, Monika H Henzinger, Sebastian Krinninger, Veronika Loitzenbauer, and Michael Raskin. “Approximating the Minimum Cycle Mean.” <i>Theoretical Computer Science</i>. Elsevier, 2014. <a href=\"https://doi.org/10.1016/j.tcs.2014.06.031\">https://doi.org/10.1016/j.tcs.2014.06.031</a>.","ista":"Chatterjee K, Henzinger MH, Krinninger S, Loitzenbauer V, Raskin M. 2014. Approximating the minimum cycle mean. Theoretical Computer Science. 547(C), 104–116.","apa":"Chatterjee, K., Henzinger, M. H., Krinninger, S., Loitzenbauer, V., &#38; Raskin, M. (2014). Approximating the minimum cycle mean. <i>Theoretical Computer Science</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.tcs.2014.06.031\">https://doi.org/10.1016/j.tcs.2014.06.031</a>","ama":"Chatterjee K, Henzinger MH, Krinninger S, Loitzenbauer V, Raskin M. Approximating the minimum cycle mean. <i>Theoretical Computer Science</i>. 2014;547(C):104-116. doi:<a href=\"https://doi.org/10.1016/j.tcs.2014.06.031\">10.1016/j.tcs.2014.06.031</a>","mla":"Chatterjee, Krishnendu, et al. “Approximating the Minimum Cycle Mean.” <i>Theoretical Computer Science</i>, vol. 547, no. C, Elsevier, 2014, pp. 104–16, doi:<a href=\"https://doi.org/10.1016/j.tcs.2014.06.031\">10.1016/j.tcs.2014.06.031</a>.","short":"K. Chatterjee, M.H. Henzinger, S. Krinninger, V. Loitzenbauer, M. Raskin, Theoretical Computer Science 547 (2014) 104–116.","ieee":"K. Chatterjee, M. H. Henzinger, S. Krinninger, V. Loitzenbauer, and M. Raskin, “Approximating the minimum cycle mean,” <i>Theoretical Computer Science</i>, vol. 547, no. C. Elsevier, pp. 104–116, 2014."},"department":[{"_id":"KrCh"}],"article_processing_charge":"No","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1307.4473"]},"project":[{"call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407","call_identifier":"FWF","name":"Game Theory"},{"grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7"},{"_id":"2587B514-B435-11E9-9278-68D0E5697425","name":"Microsoft Research Faculty Fellowship"}],"status":"public","page":"104 - 116","language":[{"iso":"eng"}],"intvolume":"       547","publist_id":"5836","oa_version":"Preprint","issue":"C","quality_controlled":"1","scopus_import":"1","title":"Approximating the minimum cycle mean","main_file_link":[{"url":"http://arxiv.org/abs/1307.4473","open_access":"1"}],"date_published":"2014-08-28T00:00:00Z","day":"28","publisher":"Elsevier","article_type":"original","year":"2014","ec_funded":1}