We propose a new algorithm to obtain max flow for the multicommodity flow.
This algorithm utilizes the max-flow min-cut theorem and the well known
labeling algorithm due to Ford and Fulkerson [1]. We proceed as follows: We
select one source/sink pair among the n distinguished source/sink pairs at a
time and treat the given multicommodity network as a single commodity network
for such chosen source/sink pair. Then applying standard labeling algorithm,
separately for each sink/source pair, the feasible flow which is max flow and
the corresponding minimum cut corresponding to each source/sink pair is
obtained. A record is made of these cuts and the paths flowing through the
edges of these cuts. This record is then utilized to develop our algorithm to
obtain max flow for multicommodity flow. In this paper we have pinpointed the
difficulty behind getting a max flow min cut type theorem for multicommodity
flow and found out a remedy.