Tuesday, April 15, 2008

* Multicommodity Flow Problem

MULTICOMMODITY FLOW

The maximum concurrent multicommodity flow problem: Let G = (V, E) be
a directed graph with k commodities i = 1,...,k.  Commodity i has
source s_i and sink t_i.  The objective is to route, for each
commodity i, a flow of value d_i from s_i to t_i.  The congestion on
an edge cong_e = sum_i f^i_e/c_e.  The goal is to minimize max_e
cong_e.

We assume that max_e cong_e = 1.  For each edge e, define a potential
Delta^{cong_e}.  Initially all flows f_e^i are 0.