Computing mimicking networks

Abstract

A mimicking network for a k-terminal network, N, is one whose realizable external flows are the same as those of N. Let S(k) denote the minimum size of a mimicking network for a k-terminal network. In this paper we give new constructions of mimicking networks and prove the following results (the values in brackets are the previously best known results): 5(4) = 5 [216], 5(5) = 6 [232]. For bounded treewidth networks we show S(k) = 0(k) [22], and for outerplanar networks we show S(k) ≤ 10k - 6 [k 22k+2].