Editing Maximum flow problem (section)

===Multi-source multi-sink maximum flow problem===
[[File:Multi-source multi-sink flow problem.svg|thumb|right|Fig. 4.1.1. Transformation of a multi-source multi-sink maximum flow problem into a single-source single-sink maximum flow problem]]
Given a network <math>N = (V, E)</math> with a set of sources <math>S = \{s_1, \ldots, s_n\}</math> and a set of sinks <math>T = \{t_1, \ldots, t_m\}</math> instead of only one source and one sink, we are to find the maximum flow across <math>N</math>. We can transform the multi-source multi-sink problem into a maximum flow problem by adding a ''consolidated source'' connecting to each vertex in <math>S</math> and a ''consolidated sink ''connected by each vertex in <math>T</math> (also known as ''supersource'' and ''supersink'') with infinite capacity on each edge (See Fig. 4.1.1.).