Approximating the minimum cycle mean Chatterjee, Krishnendu ; https://orcid.org/0000-0002-4561-241X Henzinger, Monika H ; https://orcid.org/0000-0002-5008-6530 Krinninger, Sebastian Loitzenbauer, Veronika Raskin, Michael 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. Elsevier 2014 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/1375 Chatterjee K, Henzinger M, 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2014.06.031 info:eu-repo/semantics/altIdentifier/wos/000340694000008 info:eu-repo/semantics/altIdentifier/arxiv/1307.4473 info:eu-repo/semantics/openAccess