Oblivious routing for the Lp-norm

Matthias Englert, Harald Räcke

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations

Abstract

Gupta et al. [13] introduced a very general multi-commodity 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 ℓ, 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 Ω(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 Li-norm while the result of Räcke [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.

Original languageEnglish
Title of host publicationProceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Pages32-40
Number of pages9
DOIs
StatePublished - 2009
Externally publishedYes
Event50th Annual Symposium on Foundations of Computer Science, FOCS 2009 - Atlanta, GA, United States
Duration: 25 Oct 200927 Oct 2009

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Country/TerritoryUnited States
CityAtlanta, GA
Period25/10/0927/10/09

Keywords

  • Metric embeddings
  • Norm
  • Oblivious routing

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