Datensatz

Zusammenfassung

A {\em 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 $S(k) \leq 10k-6~[k^22^{k+2}]$.