The projected pairwise multicommodity flow polyhedron

Multicommodity Flow

Leighton and Rao use multicommodity flow results to design the first polynomial time approximation algorithms for well known NP-Hard optimization problems. Such problems include graph partitioning, crossing number, VLSI layout, and many more. Furthermore, Leighton and Rao are responsible for establishing the max-flow min-cut theorems on multicommodity flow problems, which lead to the algorithms...

Multicommodity Network Flow Problems

In this paper, we consider to apply a primal-dual proximal point algorithm to the multicommodity network flow problem. A remarkable feature of the algorithm consists in how to find an approximate saddle point of the augmented Lagrangian of the problem. In particular, at each iteration, an approximate solution of the subproblem always satisfies the flow conservation equations for all commodities...

0.1 Multicommodity Flow

In this lecture we consider multicommodity network flows. As usual, we assume an ergodic Markov chain P whose stationary distribution is π. We say that an edge e = (z, z′) has capacity C(e) := π(z)P (z, z′). Note that π(z)P (z, z′) is also called the ergodic flow from z to z′. It represents the flow of probability mass along the edge when the Markov chain is at stationarity. For all pairs (x, y...

Approximation Algorithms for Multicommodity Flow

Multicommodity Flow and Circuit Switching

Given a set of request pairs in a network, the problem of routing virtual circuits with low congestion is to connect each pair by a path so that few paths use the same link in the network. We build on an earlier multicommodity ow based approach of Leighton & Rao to show that \short" ow-paths lead to path-selections with \low" congestion. This shows that such good path-selections exist for const...