Synthesis of Networks

Abstract

Up to now, we have only considered flows or circulations, respectively, for a given network. However, the converse question is very interesting, too: For given conditions on the flow, construct a network (with as little effort as possible) on which such a flow would be possible. On the one hand, we consider the case where all edges can be built with the same cost and we are looking for an undirected network with lower bounds on the maximal values of a flow between any two vertices. We analyze such ‘symmetric networks’ via ‘equivalent flow trees’ and ‘equivalent cut trees’. This technique has an interesting application for the construction of certain communication networks; this is discussed in Section 10.4. On the other hand, we look at the question of how to increase the maximal value of the flow for a given flow network by increasing the capacities of some edges as economically as possible.