Approximating the minimum cycle mean
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 in O(n^2) time to the problem of a logarithmic number of min-plus matrix multiplications of n-by-n matrices, where n is the number of vertices of the graph. (2) Second, when the weights are nonnegative, we present the first (1 + {\epsilon})-approximation algorithm for the problem and the running time of our algorithm is \tilde(O)(n^\omega log^3(nW/{\epsilon}) / {\epsilon}), where O(n^\omega) is the time required for the classic n-by-n matrix multiplication and W is the maximum value of the weights.
Cite
@article{arxiv.1307.4473,
title = {Approximating the minimum cycle mean},
author = {Krishnendu Chatterjee and Monika Henzinger and Sebastian Krinninger and Veronika Loitzenbauer},
journal= {arXiv preprint arXiv:1307.4473},
year = {2013}
}
Comments
In Proceedings GandALF 2013, arXiv:1307.4162