@article{1375,
  abstract     = {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.},
  author       = {Chatterjee, Krishnendu and Henzinger, Monika H and Krinninger, Sebastian and Loitzenbauer, Veronika and Raskin, Michael},
  journal      = {Theoretical Computer Science},
  number       = {C},
  pages        = {104 -- 116},
  publisher    = {Elsevier},
  title        = {{Approximating the minimum cycle mean}},
  doi          = {10.1016/j.tcs.2014.06.031},
  volume       = {547},
  year         = {2014},
}