TY - GEN
T1 - Optimal Error Resilience of Adaptive Message Exchange
AU - Efremenko, Klim
AU - Kol, Gillat
AU - Saxena, Raghuvansh R.
N1 - Funding Information:
Klim Efremenko is supported by the Israel Science Foundation (ISF) through grant No. 1456/18. Gillat Kol is supported by an Alfred P. Sloan Fellowship, the National Science Foundation CAREER award CCF-1750443, and by the E. Lawrence Keyes Jr. / Emerson Electric Co. Award. Raghuvansh R. Saxena is supported by the National Science Foundation CAREER award CCF-1750443.
Publisher Copyright:
© 2021 ACM.
PY - 2021/6/15
Y1 - 2021/6/15
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 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.
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 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.
KW - Communication Complexity
KW - Error Resilience
KW - Interactive Coding
UR - http://www.scopus.com/inward/record.url?scp=85108151366&partnerID=8YFLogxK
U2 - 10.1145/3406325.3451077
DO - 10.1145/3406325.3451077
M3 - Conference contribution
AN - SCOPUS:85108151366
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 1235
EP - 1247
BT - STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
A2 - Khuller, Samir
A2 - Williams, Virginia Vassilevska
PB - Association for Computing Machinery
T2 - 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Y2 - 21 June 2021 through 25 June 2021
ER -