Edge removal in undirected networks

Michael Langberg; Michelle Effros

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arXiv · 2005.10315

Edge removal in undirected networks

Michael Langberg·Michelle Effros

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Abstract

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 $\lambda$. In this short manuscript, 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.

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Michael Langberg, Michelle Effros. 2020-05-20. Edge removal in undirected networks. https://arxiv.org/abs/2005.10315

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