A Fast Distributed Algorithm for -Fair Packing Problems

Over the past two decades, fair resource allocation problems 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). It converges to approximate solutions in running times that have an inverse polynomial dependence on the approximation parameter . The convergence time has polylogarithmic dependence on the problem size for , and a nearly-linear dependence on the number of variables for . These are the best convergence times known for these problems.
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