5 research outputs found
A Fast Distributed Stateless Algorithm for -Fair Packing Problems
Over the past two decades, fair resource allocation problems have received
considerable attention in a variety of application areas. However, little
progress has been made in the design of distributed algorithms with convergence
guarantees for general and commonly used -fair allocations. In this
paper, we study weighted -fair packing problems, that is, the problems
of maximizing the objective functions (i) when , and (ii) 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 that converges to an
approximate solution in time (number of distributed iterations)
that has an inverse polynomial dependence on the approximation parameter
and poly-logarithmic dependence on the problem size. This is the
first distributed algorithm for weighted fair packing with
poly-logarithmic convergence in the input size. The algorithm uses simple local
update rules and is stateless (namely, it allows asynchronous updates, is
self-stabilizing, and allows incremental and local adjustments). We also obtain
a number of structural results that characterize fair allocations as
the value of is varied. These results deepen our understanding of
fairness guarantees in fair packing allocations, and also provide
insight into the behavior of fair allocations in the asymptotic cases
, , and .Comment: Added structural results for asymptotic cases of \alpha-fairness
(\alpha approaching 0, 1, or infinity), improved presentation, and revised
throughou