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): S(4)=5 [2 ¹⁶ ] , S(5)=6 [2 ³² ] . For bounded treewidth networks we show S(k)= O(k) [2^ 2 ^k ] , and for outerplanar networks we show S(k) $\leq$ 10k-6 [k ² 2 ^k+2 ] .