A dispersion theorem for communication networks based on term sets

Traditionally, communication networks are modeled and analyzed in terms of information flows in graphs. In this paper, we introduce a new symbolic approach to communication networks, where the topology of the underlying network is contained in a set of formal terms. To any choice of coding functions we associate a measure of performance, referred to as the dispersion. Many communication problems can be recast as dispersion problems in this setup. We state and prove variants of a theorem concerning dispersion of information in communication networks which generalizes the network coding theorem. The dispersion theorem resembles the max-flow min-cut theorem for commodity networks and states that the minimal cut value can be asymptotically achieved by the use of coding functions based on a routing scheme that uses dynamic headers.