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Why locally-fair maximal flows in client-server networks perform well

JOURNAL OF COMBINATORIAL OPTIMIZATION 2011年第3期22卷 426-437页

作者： Berman, Kenneth A. Yoshikawa, Chad Univ Cincinnati Dept Comp Sci Cincinnati OH 45221 USA

Maximal flows reach at least a 1/2 approximation of the maximum flow in client-server networks. By adding 1 additional time round to any distributed maximal flow algorithm we show how this 1/2-approximation can be improved on bounded-degree networks. We call these modified maximal flows 'locally fair' since there is a measure of fairness prescribed to each client and server in the network. Let N=(U,V,E,b) represent a client-server network with clients U, servers V, network links E, and node capacities b, where we assume that each capacity is at least one unit. Let d(u) denote the b-weighted degree of any node uaUa(a)V, Delta=max {d(u)|uaU} and delta=min {d(v)|vaV}. We show that a locally-fair maximal flow f achieves an approximation to the maximum flow of min{1, Delta(2)-delta/2 Delta(2)-delta Delta-Delta}, and this result is sharp for any given integers delta and Delta. This results are of practical importance since local-fairness loosely models the steady-state behavior of TCP/IP and these types of degree-bounds often occur naturally (or are easy to enforce) in real client-server systems.

关键词： distributed flow algorithms Oblivious routing Network algorithms Maximal flow

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Why Locally-Fair Maximal flows in Client-Server Networks Perform Well

Why Locally-Fair Maximal Flows in Client-Server Networks Per...

引用

15th Annual International Conference on Computing and Combinatorics (COCOON 2009)

作者： Berman, Kenneth A. Yoshikawa, Chad Univ Cincinnati Dept Comp Sci Cincinnati OH 45221 USA

ISBN: (纸本)9783642028816

Maximal flows reach at least a 1/2 approximation of the maximum flow in client-server networks. By adding only I additional time round to any distributed maximal flow algorithm we show how this 1/2-approximation can be improved on bounded-degree networks. We call these modified maximal flows 'locally fair' since there is a measure of fairness prescribed to each client and server in the network. Let N = (U, V, E, b) represent a client-server network with clients U, servers V, network links E, and node capacities b, where we assume that each capacity is at least one unit. Let d(u) denote the b-weighted degree of any node u is an element of U boolean OR V, Delta = max{d(u)vertical bar u is an element of U} and delta = min{d(v)vertical bar v is an element of V}. We show that a locally-fair maximal flow f achieves an approximation to the maximum flow of min{1, Delta(2)-delta/2 Delta(2)-delta Delta-Delta} and this result is sharp for any given integers delta and Delta. This results are of practical importance since local-fairness loosely models the steady-state behavior of TCP/IP and these types of degree-bounds often occur naturally (or are easy to enforce) in real client-server systems.

关键词： distributed flow algorithms Oblivious Routing Network algorithms Maximal flow

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