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In this paper, the authors develop a fast resource allocation algorithm that takes advantage of intra-session network coding. The algorithm maximizes the total utility of multiple unicast (or multicast) sessions subject to capacity constraints, where packets are coded within each session. The solution is a primal solution that does not use duality or congestion prices. Thus, it does not require building up queues to achieve the optimal resource allocation. Hence, the queueing delay of the packets can be tightly controlled. The existing primal solution in the literature requires a separate graph-theoretic algorithm to find the min-cut of each session, whose complexity grows quadratically with the total number of nodes.
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