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 language | English |
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| Title of host publication | 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 1421-1426 |
| Number of pages | 6 |
| ISBN (Electronic) | 9781538682098 |
| DOIs | |
| State | Published - 12 Jul 2021 |
| Externally published | Yes |
| Event | 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia Duration: 12 Jul 2021 → 20 Jul 2021 |
Publication series
| Name | IEEE International Symposium on Information Theory - Proceedings |
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| Volume | 2021-July |
| ISSN (Print) | 2157-8095 |
Conference
| Conference | 2021 IEEE International Symposium on Information Theory, ISIT 2021 |
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| Country/Territory | Australia |
| City | Virtual, Melbourne |
| Period | 12/07/21 → 20/07/21 |
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.