TY - BOOK
T1 - Optimal Error Resilience of Adaptive Message Exchange
AU - Efremenko, Klim
AU - Kol, Gillat
AU - Saxena, Raghuvansh
N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2021/4/8
Y1 - 2021/4/8
N2 - 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 [BR11], STOC 2011). The problem was also studied over the adaptive channel, where the order in which the parties communicate may not be predetermined ([GHS14], STOC 2014; [EKS20], 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.
AB - 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 [BR11], STOC 2011). The problem was also studied over the adaptive channel, where the order in which the parties communicate may not be predetermined ([GHS14], STOC 2014; [EKS20], 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.
M3 - Report
VL - 60
BT - Optimal Error Resilience of Adaptive Message Exchange
ER -