|| Edge removal in undirected networks
||Michael Langberg, University at Buffalo, United States; Michelle Effros, Caltech, United States|
||D3-S7-T1: Topics in Network Coding II
||Thursday, 15 July, 00:00 - 00:20
||Thursday, 15 July, 00:20 - 00:40
The edge-removal problem asks whether the removal of a $\lambda$-capacity edge from a given network can decrease the communication rate between source-terminal pairs by more than $\lambda$. We prove that for undirected networks, removing a $\lambda$ capacity edge decreases the rate by $O(\lambda)$. Through previously known reductive arguments, here newly applied to undirected networks, our result implies that the zero-error capacity region of an undirected network equals its vanishing-error capacity region. Whether it is possible to prove similar results for directed networks remains an open question.