Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6876143 | Theoretical Computer Science | 2014 | 13 Pages |
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 nÃn-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 OË(nÏlog3(nW/ϵ)/ϵ),1 where O(nÏ) is the time required for the classicnÃn-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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Krishnendu Chatterjee, Monika Henzinger, Sebastian Krinninger, Veronika Loitzenbauer, Michael A. Raskin,