Oblivious routing for the Lp-norm

Matthias Englert, Harald Räcke

Publikation: Beitrag in Buch/Bericht/KonferenzbandKonferenzbeitragBegutachtung

17 Zitate (Scopus)

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.

OriginalspracheEnglisch
TitelProceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Seiten32-40
Seitenumfang9
DOIs
PublikationsstatusVeröffentlicht - 2009
Extern publiziertJa
Veranstaltung50th Annual Symposium on Foundations of Computer Science, FOCS 2009 - Atlanta, GA, USA/Vereinigte Staaten
Dauer: 25 Okt. 200927 Okt. 2009

Publikationsreihe

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

Konferenz

Konferenz50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Land/GebietUSA/Vereinigte Staaten
OrtAtlanta, GA
Zeitraum25/10/0927/10/09

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