Optimal error resilience of adaptive message exchange

Klim Efremenko, Gillat Kol, Raghuvansh R. Saxena

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the error resilience of the message exchange task: Two parties, each holding a private input, want to exchange their inputs. However, the channel connecting them is governed by an adversary that may corrupt a constant fraction of the transmissions. What is the maximum fraction of corruptions that still allows the parties to exchange their inputs? For the non-adaptive channel, where the parties must agree in advance on the order in which they communicate, the maximum error resilience was shown to be 1/4 (see Braverman and Rao, STOC 2011). The problem was also studied over the adaptive channel, where the order in which the parties communicate may not be predetermined (Ghaffari, Haeupler, and Sudan, STOC 2014; Efremenko, Kol, and Saxena, STOC 2020). These works show that the adaptive channel admits much richer set of protocols but leave open the question of finding its maximum error resilience. In this work, we show that the maximum error resilience of a protocol for message exchange over the adaptive channel is 5/16, thereby settling the above question. Our result requires improving both the known upper bounds and the known lower bounds for the problem.

Original languageEnglish (US)
Title of host publicationSTOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
EditorsSamir Khuller, Virginia Vassilevska Williams
PublisherAssociation for Computing Machinery
Pages1235-1247
Number of pages13
ISBN (Electronic)9781450380539
DOIs
StatePublished - Jun 15 2021
Event53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy
Duration: Jun 21 2021Jun 25 2021

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/TerritoryItaly
CityVirtual, Online
Period6/21/216/25/21

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • Communication Complexity
  • Error Resilience
  • Interactive Coding

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