[{"volume":547,"date_created":"2018-12-11T11:51:40Z","day":"28","oa":1,"_id":"1375","quality_controlled":"1","publisher":"Elsevier","date_updated":"2020-08-11T10:09:08Z","abstract":[{"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.","lang":"eng"}],"department":[{"_id":"KrCh"}],"title":"Approximating the minimum cycle mean","oa_version":"Submitted Version","page":"104 - 116","type":"journal_article","publication_status":"published","date_published":"2014-08-28T00:00:00Z","language":[{"iso":"eng"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","scopus_import":1,"status":"public","month":"08","main_file_link":[{"url":"http://arxiv.org/abs/1307.4473","open_access":"1"}],"intvolume":" 547","issue":"C","year":"2014","publication":"Theoretical Computer Science","citation":{"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.","short":"K. Chatterjee, M. Henzinger, S. Krinninger, V. Loitzenbauer, M. Raskin, Theoretical Computer Science 547 (2014) 104–116.","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.","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","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.","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"},"doi":"10.1016/j.tcs.2014.06.031","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"},{"name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307"},{"_id":"2587B514-B435-11E9-9278-68D0E5697425","name":"Microsoft Research Faculty Fellowship"}],"publist_id":"5836","author":[{"last_name":"Chatterjee","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"last_name":"Henzinger","first_name":"Monika","full_name":"Henzinger, Monika"},{"full_name":"Krinninger, Sebastian","last_name":"Krinninger","first_name":"Sebastian"},{"full_name":"Loitzenbauer, Veronika","first_name":"Veronika","last_name":"Loitzenbauer"},{"first_name":"Michael","last_name":"Raskin","full_name":"Raskin, Michael"}]}]