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.
|Title of host publication||2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||6|
|State||Published - 12 Jul 2021|
|Event||2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia|
Duration: 12 Jul 2021 → 20 Jul 2021
|Name||IEEE International Symposium on Information Theory - Proceedings|
|Conference||2021 IEEE International Symposium on Information Theory, ISIT 2021|
|Period||12/07/21 → 20/07/21|
Bibliographical noteFunding Information:
M. Langberg is with the Department of Electrical Engineering at the University at Buffalo (State University of New York). Email: firstname.lastname@example.org M. Effros is with the Department of Electrical Engineering at the California Institute of Technology. Email: email@example.com This work is supported in part by NSF grants CCF-1817241 and CCF-1909451. The full version of this work appears in .
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