Approximation algorithms for the general max-min resource sharing problem: Faster and simpler

We propose an approximation algorithm for the general max-min resource sharing problem with M nonnegative concave constraints on a convex set B. The algorithm is based on a Lagrangian decomposition method and it uses a c - approximation algorithm (called approximate block solver) for a simpler maximization problem over the convex set B. We show that our algorithm achieves within O(M(ln M + epsilon(-2) ln epsilon(-1))) iterations or calls to the approximate block solver a solution for the general max-min resource sharing problem with approximation ratio c/(1 - epsilon). The algorithm is faster and simpler than the previous known approximation algorithms for the problem.