--- _id: '1375' 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.' article_processing_charge: No article_type: original author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Sebastian full_name: Krinninger, Sebastian last_name: Krinninger - first_name: Veronika full_name: Loitzenbauer, Veronika last_name: Loitzenbauer - first_name: Michael full_name: Raskin, Michael last_name: Raskin citation: ama: Chatterjee K, Henzinger MH, 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. H., Krinninger, S., Loitzenbauer, V., & Raskin, M. (2014). Approximating the minimum cycle mean. Theoretical Computer Science. Elsevier. https://doi.org/10.1016/j.tcs.2014.06.031 chicago: Chatterjee, Krishnendu, Monika H Henzinger, Sebastian Krinninger, Veronika Loitzenbauer, and Michael Raskin. “Approximating the Minimum Cycle Mean.” Theoretical Computer Science. Elsevier, 2014. https://doi.org/10.1016/j.tcs.2014.06.031. ieee: K. Chatterjee, M. H. Henzinger, S. Krinninger, V. Loitzenbauer, and M. Raskin, “Approximating the minimum cycle mean,” Theoretical Computer Science, vol. 547, no. C. Elsevier, pp. 104–116, 2014. ista: Chatterjee K, Henzinger MH, 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. short: K. Chatterjee, M.H. Henzinger, S. Krinninger, V. Loitzenbauer, M. Raskin, Theoretical Computer Science 547 (2014) 104–116. date_created: 2018-12-11T11:51:40Z date_published: 2014-08-28T00:00:00Z date_updated: 2022-09-09T11:50:58Z day: '28' department: - _id: KrCh doi: 10.1016/j.tcs.2014.06.031 ec_funded: 1 external_id: arxiv: - '1307.4473' intvolume: ' 547' issue: C language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1307.4473 month: '08' oa: 1 oa_version: Preprint page: 104 - 116 project: - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 2587B514-B435-11E9-9278-68D0E5697425 name: Microsoft Research Faculty Fellowship publication: Theoretical Computer Science publication_status: published publisher: Elsevier publist_id: '5836' quality_controlled: '1' scopus_import: '1' status: public title: Approximating the minimum cycle mean type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 547 year: '2014' ...