Edge removal in undirected networks

Michael Langberg, Michelle Effros

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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. 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.

Original languageEnglish
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1421-1426
Number of pages6
ISBN (Electronic)9781538682098
DOIs
StatePublished - 12 Jul 2021
Externally publishedYes
Event2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia
Duration: 12 Jul 202120 Jul 2021

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2021-July
ISSN (Print)2157-8095

Conference

Conference2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/TerritoryAustralia
CityVirtual, Melbourne
Period12/07/2120/07/21

Bibliographical note

Funding Information:
M. Langberg is with the Department of Electrical Engineering at the University at Buffalo (State University of New York). Email: mikel@buffalo.edu M. Effros is with the Department of Electrical Engineering at the California Institute of Technology. Email: effros@caltech.edu This work is supported in part by NSF grants CCF-1817241 and CCF-1909451. The full version of this work appears in [1].

Publisher Copyright:
© 2021 IEEE.

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