Approximating the minimum cycle mean
نویسندگان
چکیده
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(n2) time 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(nω log3 (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.
منابع مشابه
Approximating the Expected Values for Combinatorial Optimization Problems over Stochastic Points
We consider the stochastic graph model where the location of each vertex is a random point in a given metric space. We study the problems of computing the expected lengths of the minimum spanning tree, the minimum perfect matching and the minimum cycle cover on such a stochastic graph and obtain an FPRAS (Fully Polynomial Randomized Approximation Scheme) for each of these problems. Our result f...
متن کاملApproximate Minimum Bit - Error Rate Multiuser Detection
— The minimum mean-squared-error (MMSE) linear multiuser detector [1–2] is popular because of its good performance and amenability to adaptive implementation. However , there are circumstances in which the linear detector that minimizes bit-error rate (BER) can significantly outperform the MMSE detector. We propose a low-complexity adaptive algorithm for approximating the minimum-BER linear mul...
متن کاملA note on finding minimum mean cycle
In a directed graph with edge weights, the mean weight of a directed cycle is the weight of its edges divided by their number. The minimum cycle mean of the graph is the minimum mean weight of a cycle. Karp gave a characterization of minimum cycle mean and an O(nm) algorithm to compute it, where n is the number of vertices and m is the number of edges. However, an algorithm he suggested for ide...
متن کاملApproximability of Minimum-weight Cycle Covers
A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L ⊆ N. For most sets L, computing L-cycle covers of minimum weight is NP-hard and APX-hard. While computing L-cycle covers of maximum weight admits constant factor approximation algorithms (both for undirected and dir...
متن کامل