TY - GEN
T1 - Time and communication efficient consensus for crash failures
AU - Chlebus, Bogdan S.
AU - Kowalski, Dariusz R.
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2006
Y1 - 2006
N2 - This paper is about consensus solutions optimized simultaneously for the time and communication complexities. Synchronous message passing with processors prone to crashes is the computing environment. The number f of crashes can be arbitrary as long as it is smaller than the number n of processors in the system. As a building block to our consensus solutions, we consider the gossiping problem in which processors have input rumors and the goal of every processor is to learn all the rumors of the processors that have not crashed. We show that gossiping can be achieved by a deterministic algorithm working in script O sign(log3 n) time and sending script O sign(n log 4 n) point-to-point messages. These results improve upon the best previously known deterministic solution of gossiping that operated in script O sign(log2 n) time and generated script O sign(n1+ε) messages, for any constant ε > 0. The efficient gossiping algorithm is applied to the problem of reaching consensus. In the Consensus problem, each processor starts with its input value and the goal is to have all processors agree on exactly one value among the inputs. First we develop a deterministic algorithm solving Consensus in script O sign(n) time while sending script O sign(n log5 n) messages. The best previously known algorithms solving Consensus in script O sign(n) time had the message complexity bounded by script O sign(n1+ε), for any constant ε > 0. Next we improve the Consensus solution so that it is early stopping, which means that it terminates in script O sign(f + 1) time, where f is the number of crashes in an execution, while preserving the message complexity script O sign(n log 5 n).
AB - This paper is about consensus solutions optimized simultaneously for the time and communication complexities. Synchronous message passing with processors prone to crashes is the computing environment. The number f of crashes can be arbitrary as long as it is smaller than the number n of processors in the system. As a building block to our consensus solutions, we consider the gossiping problem in which processors have input rumors and the goal of every processor is to learn all the rumors of the processors that have not crashed. We show that gossiping can be achieved by a deterministic algorithm working in script O sign(log3 n) time and sending script O sign(n log 4 n) point-to-point messages. These results improve upon the best previously known deterministic solution of gossiping that operated in script O sign(log2 n) time and generated script O sign(n1+ε) messages, for any constant ε > 0. The efficient gossiping algorithm is applied to the problem of reaching consensus. In the Consensus problem, each processor starts with its input value and the goal is to have all processors agree on exactly one value among the inputs. First we develop a deterministic algorithm solving Consensus in script O sign(n) time while sending script O sign(n log5 n) messages. The best previously known algorithms solving Consensus in script O sign(n) time had the message complexity bounded by script O sign(n1+ε), for any constant ε > 0. Next we improve the Consensus solution so that it is early stopping, which means that it terminates in script O sign(f + 1) time, where f is the number of crashes in an execution, while preserving the message complexity script O sign(n log 5 n).
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U2 - 10.1007/11864219_22
DO - 10.1007/11864219_22
M3 - Conference contribution
AN - SCOPUS:33845210348
SN - 3540446249
SN - 9783540446248
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 314
EP - 328
BT - Distributed Computing - 20th International Symposium, DISC 2006, Proceedings
PB - Springer Verlag
T2 - 20th International Symposium on Distributed Computing, DISC 2006
Y2 - 18 September 2006 through 20 September 2006
ER -