Chatterjee, KrishnenduIST Austria ; Henzinger, Monika; 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.
Theoretical Computer Science
104 - 116
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
Chatterjee, K., Henzinger, M., 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
Chatterjee, Krishnendu, Monika 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.
K. Chatterjee, M. 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.
Chatterjee K, Henzinger M, Krinninger S, Loitzenbauer V, Raskin M. 2014. Approximating the minimum cycle mean. Theoretical Computer Science. 547(C), 104–116.
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.