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Electric routing and concurrent flow cutting Jonathan Kelner ∗ Petar Maymounkov ∗ September 15, 2009 Abstract: 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 round- ing method which we use to obtain a bound on the  1 →  1 operator norm of the inverse graph Laplacian. We show how this norm reflects both latency and congestion of electric routing. 1 Introducti on Overview We address a vision of the Internet where every participant exchanges messages with their direct frie nds and no one else . Y et such an Int ernet should be abl e to support reliable and efficient routing to remote locations identified by unchanging names in the presence of an ever changing graph of connectivity . Modestly to this end, this paper investigates the properties of routing along the electric flow in a graph (electric routing for short) for intended use in such distributed systems, whose topology changes over time. We focus on the class of expanding graphs which, we believe, gives a good trade-o ff between applic ability and precision in modeling a large class of real-wor ld networks. We address distribute d repre sentat ion and compu tation. As a measur e of perfo rmana ce, we show that electric routin g, being an oblivious routing scheme, achieves minimal maximum edge congestion (as compared to a demand- dependent optimal scheme). Furthermore, we show that electric routing continues to work (on average) in the presence of large edge failures ocurring after the routing scheme has been computed, which attests to its applicability in changing environments. We now proceed to a formal definition of oblivious routing and statement of our results . ∗ Research partially supported by NSF grant CCF-0843915. ACM Classification: F.2.2, G.2.2 AMS Classifica tion: 68Q25, 68R10 Key words and phrases: oblivious routing, spectral graph theory, Laplacian operator   a   r    X    i   v   :    0    9    0    9  .    2    8    5    9   v    1    [   c   s  .    D    M    ]    1    5    S   e   p    2    0    0    9

Tonika Routing Algorithm

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