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Published July 2021 | Submitted
Book Section - Chapter Open

Edge removal in undirected networks

Abstract

The edge-removal problem asks whether the removal of a λ-capacity edge from a given network can decrease the communication rate between source-terminal pairs by more than λ. We prove that for undirected networks, removing a λ capacity edge decreases the rate by O(λ). 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.

Additional Information

© 2021 IEEE. This work is supported in part by NSF grants CCF-1817241 and CCF-1909451. The full version of this work appears in [1].

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