Electric Routing and Concurrent Flow Cutting

We investigate an oblivious routing scheme amenable to distributed computation and resilient to graph changes, based on electrical flow. Our main technical contribution is a new rounding method which we use to obtain a bound on the L 1?L 1 operator norm of the inverse graph Laplacian.

[1]  Mikkel Thorup,et al.  Compact name-independent routing with minimum stretch , 2004, SPAA '04.

[2]  Peter G. Doyle,et al.  Random Walks and Electric Networks: REFERENCES , 1987 .

[3]  Mohammad Taghi Hajiaghayi,et al.  New lower bounds for oblivious routing in undirected graphs , 2006, SODA '06.

[4]  Frank Thomson Leighton,et al.  Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms , 1999, JACM.

[5]  Daniel A. Spielman.  Graphs and networks , 2007 .

[6]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[7]  G. Lawler,et al.  Mixing times and e p bounds for oblivious routing , 2009 .

[8]  Mikkel Thorup,et al.  Compact name-independent routing with minimum stretch , 2008, ACM Trans. Algorithms.

[9]  Mikkel Thorup,et al.  Approximate distance oracles , 2001, JACM.

[10]  Navin Goyal,et al.  Expanders via random spanning trees , 2008, SODA.

[11]  Harald Räcke,et al.  Optimal hierarchical decompositions for congestion minimization in networks , 2008, STOC.

[12]  Ittai Abraham,et al.  On space-stretch trade-offs: lower bounds , 2006, SPAA '06.

[13]  Nikhil Srivastava,et al.  Graph sparsification by effective resistances , 2008, SIAM J. Comput..

[14]  Thomas P. Hayes,et al.  Minimizing average latency in oblivious routing , 2008, SODA '08.

[15]  Yuval Peres,et al.  Noise Tolerance of Expanders and Sublinear Expander Reconstruction , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[16]  John R. Douceur,et al.  The Sybil Attack , 2002, IPTPS.

[17]  Hariharan Narayanan,et al.  Mixing times and ℓpbounds for Oblivious routing , 2009 .

[18]  Ding-Zhu Du,et al.  Electric routing and concurrent flow cutting , 2009 .

[19]  I. Anderson,et al.  Graphs and Networks , 1981, The Mathematical Gazette.