Bandwidth allocation in networks: a single dual update subroutine for multiple objectives

Authors:
Sung-woo Cho;Ashish Goel
Affiliations:
Department of Computer Science, University of Southern, California;Department of Management Science and Engineering and (by courtesy) Computer Science, Stanford University
Venue:
CAAN'04 Proceedings of the First international conference on Combinatorial and Algorithmic Aspects of Networking
Year:
2004

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Abstract

We study the bandwidth allocation problem Maximize U(x), subject to Ax ≤ c; x ≥ 0 where U is a utility function, x is a bandwidth allocation vector, and Ax ≤ c represent the capacity constraints. We consider the class of canonical utility functions, consisting of functions U that are symmetric, non-decreasing, concave, and satisfy U(0) = 0. We present a single dual update subroutine that results in a primal solution which is a logarithmic approximation, simultaneously, for all canonical utility functions. The dual update subroutine lends itself to an efficient distributed implementation. We then employ the fractional packing framework to prove that at most O(m log m) iterations of the dual update subroutine are required; here m is the number of edges in the network.