Only the source’s and sink’s neighborhood matters: convergence results for unicast and multicast connections on random graphs and hypergraphs.

Abstract

Copyright © 2013 ICST. We study the maximum flow on random weighted directed graphs and hypergraphs, that generalize Erdös-Rényi graphs. We show that, for a single unicast connection chosen at random, its capacity, determined by the max-flow between source and sink, converges in probability to the capacity around the source or sink. Using results from network coding, we generalize this result to different types multicast connections, whose capacity is given by the max-flow between the source(s) and sinks. Our convergence results indicate that the capacity of unicast and multicast connections using network coding are, with high probability, unaffected by network size in random networks. Our results generalize to networks with random erasures.