A practical algorithm for constructing oblivious routing schemes

In a (randomized) oblivious routing scheme the path chosen for a request between a source s and a target t is independent from the current traffic in the network. Hence, such a scheme consists of probability distributions over s-t paths for every source-target pair s,t in the network.In a recent result [11] it was shown that for any undirected network there is an oblivious routing scheme that achieves a polylogarithmic competitive ratio with respect to congestion. Subsequently, Azar et al. [4] gave a polynomial time algorithm that for a given network constructs the best oblivious routing scheme, i.e. the scheme that guarantees the best possible competitive ratio. Unfortunately, the latter result is based on the Ellipsoid algorithm; hence it is unpractical for large networks.In this paper we present a combinatorial algorithm for constructing an oblivious routing scheme that guarantees a competitive ratio of O(log4n) for undirected networks. Furthermore, our approach yields a proof for the existence of an oblivious routing scheme with competitive ratio O(log3n), which is much simpler than the original proof from [11].

[1]  Philip N. Klein,et al.  Excluded minors, network decomposition, and multicommodity flow , 1993, STOC.

[2]  Allan Borodin,et al.  Routing, merging and sorting on parallel models of computation , 1982, STOC '82.

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

[4]  G. Miller,et al.  Solving Symmetric Diagonally-Dominant Systems by Preconditioning , 2003 .

[5]  Amos Fiat,et al.  On-line load balancing with applications to machine scheduling and virtual circuit routing , 1993, STOC.

[6]  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.

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

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

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

[10]  Ojas Parekh,et al.  Finding effective support-tree preconditioners , 2005, SPAA '05.

[11]  B. E. Eckbo,et al.  Appendix , 1826, Epilepsy Research.

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

[13]  Yuval Rabani,et al.  An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm , 1998, SIAM J. Comput..

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

[15]  Edith Cohen,et al.  Optimal oblivious routing in polynomial time , 2003, STOC '03.