Summary
We investigate the message complexity of distributed computations on rings of asynchronous processors. In such computations, each processor has an initial local value and the task is to compute some predetermined function of all local values. Our work deviates from previous works concerning the complexity of ring computations in that we consider the effect oflink failures. A link is said to fail if some message sent through it never reaches its destination. We show that the message complexity of any function, which is “sensitive to all its inputs”, is Θ (n logn) whenn, the number of processors, is a-priori known; and is Θ(n 2) whenn is not known. Interestingly, these tight bounds do not depend on whether the identity of a leader is a-priori known before the computation starts. These results stand in sharp contrast to the situation in asynchronous rings with no link failures, where the message complexity is affected by the a-priori knowledge of a leader but is not affected by the knowledge ofn.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Attiya H, Snir M, Warmuth M: Computing on an anonymous ring or the inherent cost of symmetry. JACM 35 (4):845–875 (1988)
Awerbuch B, Even S: A formal approach to a communication-network protocol: broadcast as a case study. EE PUB No 459, Department of Elec Engineering, Technion, Israel, (1983). An extended abstract appeared in the 3rd PODC, 1984, pp 278–281
Burns JE: A formal model for message passing systems. TR-91, Indiana University, 1980
Chang E, Roberts R: An improved algorithm for decentralized extrema-finding in circular configuration of processes. Commun ACM 22:281–283 (1979)
Dolev D, Klawe M, Rodeh M: AnO (n logn) unidirectional distributed algorithm for extremafinding in a circle. J Algorithms 3:245–250 (1982)
Fischer MJ: The consensus problem in unreliable distributed systems (a brief survey). YaleU/DCS/RR-273, 1983
Franklin R: On an improved algorithm for decentralized extrema-finding in circular configuration of processes. Commun ACM 25:336–337 (1982)
Frederickson GR, Lynch NA: The impact of synchronous communication on the problem of electing a leader in a ring. Proc 16th ACM Symp on Theory Of Computing, April 1984, pp 493–503
Goldreich O, Shrira L: Consultation in the presence of faults: two lower bounds. TR-355, Computer Science Department, Technion, Israel 1985
Goldreich O, Shrira L: Electing a leader in a ring with link failures. ACTA Inf 24:79–91 (1987)
Goldreich O, Shrira L: On the complexity of computation in the presence of link fault: the case of a ring. TR-654, Computer Science Department, Technion, Israel, 1990
Hirschberg DE, Sinclair JB: Decentralized extrema-finding in circular configuration of processors. Commun ACM 23:627–628 (1980)
Itai A, Rodeh M: Symmetry breaking in a distributed environment. Proc 22nd IEEE Symp on Foundation Of Computer Science, 1981, pp 150–157
Itai A, Rodeh M: The multi-tree approach to reliability in distributed networks. Proc 25th IEEE Symp on Foundation Of Computer Science, 1984, pp 137–147
LeLann G: Distributed systems — towards a formal approach. In: Gilchrist B (ed) Information Processing 77. North Holland, Amsterdam 1977, pp 155–160
Lynch NA, Fischer MJ: On describing the behavior and implementation of distributed systems. Theor Comput Sci 13:17–43 (1981)
Lynch NA, Mansour Y, Fekete A: The data link layer: two impossibility results. Proc 7th PODC, 1988, pp 149–170
Merritt M: Elections in the presence of faults. Proc 3rd PODC, 1984, pp 134–142
Peterson GL: AnO(n logn) unidirectional algorithm for the circular extrema problem. ACM Trans Program Lang Syst pp 758–762 (1982)
Shrira L, Rodeh M: Methodological construction of reliable distributed algorithms. TR-361, Computer Science Department, Technion, Israel, 1985
Vitanyi PMB: Distributed election in an archimedean ring of processors. Proc 16th ACM Symp on Theory Of Computing, April 1984, pp 542–547
Author information
Authors and Affiliations
Additional information
Oded Goldreich was born in Tel-Aviv, Israel, on February 4th 1957. Received B.A., M.Sc., and D.Sc. in Computer Science from the Technion — Israel Institute of Technology, Haifa, Israel, in 1980, 1982, and 1983, respectively. He is currently an Associate Professor of Computer Science in the Technion. From 1983 to 1986, he was a postdoctoral fellow in MIT's Laboratory for Computer Science. His research interests include cryptography and related areas, relation between randomness and algorithms, and distributed computation.
Luiba Shrira was born in Vilnius, Lithuania. Received B.A., M.Sc., and D.Sc. in Computer Science from the Technion—Israel Institute of Technology, Haifa, Israel in 1977, 1980, and 1985, respectively. from 1986 to 1989 she was a postdoctoral fellow at Laboratory for Computer science at MIT, where she is currently a Research Associate. Her research interests include highly-available and reliable distributed algorithms and systems, persistent object systems, and programming methodology.
Part of the work has been done while the first author was in the Laboratory for Computer Science of MIT and the second author was in the Computer Science Department of the Technion. First author was partially supported by a Weizmann Postdoctoral Fellowship, an IBM Postdoctoral Fellowship, and Albert Einstein Research Fund (through Technion's V.P.R. Fund)
Rights and permissions
About this article
Cite this article
Goldreich, O., Shrira, L. On the complexity of computation in the presence of link failures: the case of a ring. Distrib Comput 5, 121–131 (1991). https://doi.org/10.1007/BF02252955
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02252955