[{"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."}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","publist_id":"5836","oa_version":"Submitted Version","oa":1,"type":"journal_article","scopus_import":1,"year":"2014","publication":"Theoretical Computer Science","date_updated":"2020-08-11T10:09:08Z","month":"08","project":[{"call_identifier":"FWF","grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory","call_identifier":"FWF"},{"grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"Microsoft Research Faculty Fellowship","_id":"2587B514-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"intvolume":" 547","date_published":"2014-08-28T00:00:00Z","title":"Approximating the minimum cycle mean","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1307.4473"}],"publisher":"Elsevier","date_created":"2018-12-11T11:51:40Z","day":"28","author":[{"full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","orcid":"0000-0002-4561-241X"},{"last_name":"Henzinger","full_name":"Henzinger, Monika","first_name":"Monika"},{"last_name":"Krinninger","full_name":"Krinninger, Sebastian","first_name":"Sebastian"},{"first_name":"Veronika","last_name":"Loitzenbauer","full_name":"Loitzenbauer, Veronika"},{"first_name":"Michael","full_name":"Raskin, Michael","last_name":"Raskin"}],"publication_status":"published","volume":547,"doi":"10.1016/j.tcs.2014.06.031","page":"104 - 116","citation":{"short":"K. Chatterjee, M. Henzinger, S. Krinninger, V. Loitzenbauer, M. Raskin, Theoretical Computer Science 547 (2014) 104–116.","ama":"Chatterjee K, Henzinger M, Krinninger S, Loitzenbauer V, Raskin M. Approximating the minimum cycle mean. *Theoretical Computer Science*. 2014;547(C):104-116. doi:10.1016/j.tcs.2014.06.031","apa":"Chatterjee, K., Henzinger, M., Krinninger, S., Loitzenbauer, V., & Raskin, M. (2014). Approximating the minimum cycle mean. *Theoretical Computer Science*, *547*(C), 104–116. https://doi.org/10.1016/j.tcs.2014.06.031","chicago":"Chatterjee, Krishnendu, Monika Henzinger, Sebastian Krinninger, Veronika Loitzenbauer, and Michael Raskin. “Approximating the Minimum Cycle Mean.” *Theoretical Computer Science* 547, no. C (2014): 104–16. https://doi.org/10.1016/j.tcs.2014.06.031.","ista":"Chatterjee K, Henzinger M, Krinninger S, Loitzenbauer V, Raskin M. 2014. Approximating the minimum cycle mean. Theoretical Computer Science. 547(C), 104–116.","mla":"Chatterjee, Krishnendu, et al. “Approximating the Minimum Cycle Mean.” *Theoretical Computer Science*, vol. 547, no. C, Elsevier, 2014, pp. 104–16, doi:10.1016/j.tcs.2014.06.031.","ieee":"K. Chatterjee, M. Henzinger, S. Krinninger, V. Loitzenbauer, and M. Raskin, “Approximating the minimum cycle mean,” *Theoretical Computer Science*, vol. 547, no. C, pp. 104–116, 2014."},"quality_controlled":"1","issue":"C","status":"public","_id":"1375","department":[{"_id":"KrCh"}]}]