Englert, M. and Räcke, H. (2009) Oblivious Routing for the Lp-norm. In: Foundations of Computer Science, 2009. FOCS '09. 50th Annual IEEE Symposium on, 25-27 Oct. 2009, Atlanta, GA.

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Abstract

Gupta et al. [13] introduced a very general multicommodity flow problem in which the cost of a given flow solution on a graph G = (V, E) is calculated by first computing the link loads via a load-function �¿, that describes the load of a link as a function of the flow traversing the link, and then aggregating the individual link loads into a single number via an aggregation function agg:R|E| �¿ R. In this paper we show the existence of an oblivious routing scheme with competitive ratio O(log n) and a lower bound of �¿(log n/log log n) for this model when the aggregation function agg is an Lp-norm. Our results can also be viewed as a generalization of the work on approximating metrics by a distribution over dominating tree metrics (see e.g. [4], [5], [8]) and the work on minimum congestion oblivious routing [20], [14], [21]. We provide a convex combination of trees such that routing according to the tree distribution approximately minimizes the Lp-norm of the link loads. The embedding techniques of Bartal [4], [5] and Fakcharoenphol et al. [8] can be viewed as solving this problem in the L1-norm while the result of Racke [21] solves it for L�¿. We give a single proof that shows the existence of a good tree-based oblivious routing for any Lp-norm. For the Euclidean norm, we also show that it is possible to compute a tree-based oblivious routing scheme in polynomial time.

Item Type:	Conference or Workshop Item (Paper)
Uncontrolled Keywords:	focs oblivious routing metric embeddings norm
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions:	Faculty of Science > Computer Science
Depositing User:	Ms Saima Arif
Date Deposited:	23 Dec 2010 14:09
Last Modified:	26 Jul 2011 11:15
URI:	http://eprints.dcs.warwick.ac.uk/id/eprint/561

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