A Fast Distributed Algorithm for -Fair Packing Problems

Over the past two decades, fair resource allocation problems have received considerable attention in a variety of application areas. While polynomial time distributed algorithms have been designed for max-min fair resource allocation, the design of distributed algorithms with convergence guarantees for the more general fair allocations received little attention. In this paper, we study weighted fair packing problems, that is, the problems of maximizing the objective functions when , and when over linear constraints , , where are positive weights and and are non-negative. We consider the distributed computation model that was used for packing linear programs and network utility maximization problems. Under this model, we provide a distributed algorithm for general . The algorithm uses simple local update rules and is stateless (namely, it allows asynchronous updates, is self-stabilizing, and allows incremental and local adjustments). The algorithm converges to approximate solutions in running times that have an inverse polynomial dependence on the approximation parameter and poly-logarithmic dependence on the problem size. These are the best convergence times known for the fair packing problems.
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