Oblivious Routing for the Lp-norm
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.
Official URL: http://dx.doi.org/10.1109/FOCS.2009.52
Gupta et al.  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 Ã�Â¿, 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| Ã�Â¿ R. In this paper we show the existence of an oblivious routing scheme with competitive ratio O(log n) and a lower bound of Ã�Â¿(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. , , ) and the work on minimum congestion oblivious routing , , . 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 ,  and Fakcharoenphol et al.  can be viewed as solving this problem in the L1-norm while the result of Racke  solves it for LÃ�Â¿. 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|
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