Optimal oblivious routing in polynomial time

A recent seminal result of Racke is that for any undirected network there is an oblivious routing algorithm with a polylogarithmic competitive ratio with respect to congestion. Unfortunately, Racke's construction is not polynomial time. We give a polynomial time construction that guarantees Racke's bounds, and more generally gives the true optimal ratio for any (undirected or directed) network.

[1]  Amos Fiat,et al.  On-line routing of virtual circuits with applications to load balancing and machine scheduling , 1997, JACM.

[2]  Harald Räcke,et al.  Minimizing Congestion in General Networks , 2002, FOCS.

[3]  Stefano Leonardi,et al.  On-line Network Routing , 1996, Online Algorithms.

[4]  Marcin Bienkowski,et al.  A practical algorithm for constructing oblivious routing schemes , 2003, SPAA '03.

[5]  Prabhakar Raghavan,et al.  Randomized rounding: A technique for provably good algorithms and algorithmic proofs , 1985, Comb..

[6]  Ratul Mahajan,et al.  Measuring ISP topologies with rocketfuel , 2002, SIGCOMM 2002.

[7]  Leslie G. Valiant,et al.  Universal schemes for parallel communication , 1981, STOC '81.

[8]  Edith Cohen,et al.  Making intra-domain routing robust to changing and uncertain traffic demands: understanding fundamental tradeoffs , 2003, SIGCOMM '03.

[9]  Adam Meyerson,et al.  Online oblivious routing , 2003, SPAA '03.

[10]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[11]  Allan Borodin,et al.  Routing, Merging, and Sorting on Parallel Models of Computation , 1985, J. Comput. Syst. Sci..

[12]  Yossi Azar,et al.  Local optimization of global objectives: competitive distributed deadlock resolution and resource allocation , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[13]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

[14]  Christos Kaklamanis,et al.  Tight bounds for oblivious routing in the hypercube , 1990, SPAA '90.

[15]  Satish Rao,et al.  A polynomial-time tree decomposition to minimize congestion , 2003, SPAA '03.