V. Hadzilacos, and J.Y. Halpern, Message-optimal protocols for Byzantine agreement, Mathematical Systems Theory, 26 (1993) 41 - 102.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to develop efficient decentralized consensus protocols. Performance of the consensus protocols is usually assessed by the number of message steps required to reach a consensus by all nodes in a distributed system, and also the total number of messages incurred during the execution of the protocol [10] [12] 13] Several studies have been conducted to minimize the number of message steps (or time) and the number of messages for various communication networks distributed environments [5] 6] 13] 16] A recent survey can be found in [12] Clearly, there is a trade off on the number of message ....

....communication step, thus distinguishing our work in this paper from the one in [15] Also, we do not assume that nodes in the system will be faulty or maliciously send wrong messages to others. Readers interested in issues related to fault tolerance and Byzantine Agreement are referred to [2] 8] [10] [14] 2.2 DCP without an initiator (1 port) To facilitate our description of G 1 , it is necessary to define a partitioning tree and a balanced binary partitioning tree of a positive number. Definition 2: A partitioning tree of a positive number p is a tree where the root node is labeled with ....

V. Hadzilacos and J. Halpern. Message-Optimal Protocols for Byzantine Agreement. Technical Report RJ 7879, IBM Almaden Research Laboratory, San Jose, CA, December 1990.

....min(f 2; t 1) rounds) That is, in our new parlance, Theorem 2 [12, 8] Let the cost of a run of a consensus algorithm be the number of rounds, and f the actual number of faulty processors. Then there exists an algorithm A such that aA (f) O(1) i.e. A adapts to f ) Hadzilacos and Halpern [17] concentrated on runs that are failure free, and presented consensus algorithms with optimal number of messages for these runs. Which brings us to the other cost measure: the communication costs of such protocols, given by the total number of transmitted bits. Dolev and Reischuk [11] showed a ....

V. Hadzilacos and J. Halpern. Message-Optimal Protocols for Byzantine Agreement. Proc. 10th Annual ACM Symp. on the Principles of Distributed Computing, pp. 309-324, Montreal, Canada, August 1991.

....needs to be redone and to bound the number of checkpoints required. Checkpoint: Clearly, the algorithmic challenge is to design a checkpoint which is both fast and messageefficient. In order to achieve this goal we combine recent techniques of message efficient agreementprotocols (see [AHW92] and [HH93]) with the wellestablished idea of eventual (or early stopping) agreement ( DRS90] A similar approach was used by [CT90] to achieve an efficient reliable broadcast protocol. Note however, that these two techniques are somewhat contradictory; especially in our case where eventual agreement has to ....

V. Hadzilacos and J. Halpern, MessageOptimal Protocols for Byzantine Agreement. Math. Systems Theory 26, 41-102 (1993). (Also PODC'91).

....the power of the stronger omission and malicious adversaries. In the simple case of crash failures only the trivial lower bound of Omega Gamma n) messages has been known. It holds even in the failure free case. Exact upper and lower bounds for the failure free scenario were investigated by [AWH92, HH93]) A special variant of BA is early stopping BA (EBA) It requires the running time to be O(f 1) where f is the actual number of failures in a run. The time must be at least f 1, as was shown in [LF82, H83, DRS90, DM90] Lamport and Fischer [LF82] showed how to solve EBA in O( f 1)n 2 ) ....

V. Hadzilacos and J. Halpern, MessageOptimal Protocols for Byzantine Agreement. Math. Systems Theory 26, 41-102 (1993).

....has been established for this problem even if no failures actually occur [DS] Thus, overcoming potential faults is expensive, even though, in practice, they are rarely observed. This has led others to explore ways in which the price of fault tolerance may be reduced. Hadzilacos and Halpern [HH] have recently concentrated on runs that are failurefree; they present protocols with optimal number of messages for these runs. Dolev, Reischuk, and Strong [DRS] are concerned with protocols that take a number of rounds proportional to f , the number of failures that actually occur, rather than ....

....optimal in these measures and early stopping. A consensus protocol with optimal bit complexity is, a fortiori, optimal with respect to message complexity. Hadzilacos and Halpern have recently achieved consensus with (exact) message optimality, but only in the case of runs that are failure free [HH]. The rationale is that since failures are hopefully rare, optimality in the usual case is to be emphasized. However, in case (even few) failures do occur, their solution requires either a large round overhead (if asymptotical message optimality is to be maintained) or a loss of Omega (n) in ....

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V. Hadzilacos and J. Halpern, "Message-Optimal Protocols for Byzantine Agreement," Proc. 10th PODC, pp. 309-324, August 1991.

....total number of transmitted bits B (B (n Gamma t) t 1) 4 [DR] Convinced that communication costs are one of the dominant factors in a protocol s performance [G] in this paper we focus on optimizing these costs, in particular B, the total bit transfer. Recent work by Hadzilacos and Halpern [HH] also addresses this concern by studying the message and bit complexity of runs that are failure free. All previous protocols (e.g. BD, BDDS, BG1, BGP, LSP, MW] require B = Omega Gamma n 2 t) regardless of the value of the other parameters. The contribution of this paper is the first ....

V. Hadzilacos and J. Halpern, "Message-Optimal Protocols for Byzantine Agreement," Proc. 10th PODC, pp. 309-324, August 1991..

....an open problem. Also, given the great sensitivity of performance on the number of messages, it would be useful to obtain exact, rather than asymptotic, bounds as was the case for the problem studied in this paper. 2 As this paper was in the process of being refereed Hadzilacos and Halpern [15] answered these questions by providing tight bounds on the worst and average case failure free message complexity of binary BA protocols for all other types of failures that are considered in the literature on the BA problem. They also consider the case of non binary BA; among other results, they ....

Hadzilacos, V. and J.Y. Halpern. "Message-Optimal Protocols for Byzantine Agreement ". Forthcoming, 1990.

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V. Hadzilacos, and J.Y. Halpern, Message-optimal protocols for Byzantine agreement, Mathematical Systems Theory, 26 (1993) 41 - 102.

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V. Hadzilacos and J. Y. Halpern. Message-optimal protocols for Byzantine agreement. Mathematical Systems Theory, 26(1):41--102, 1993.

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Vassos Hadzilacos and Joseph Y. Halpern. Message-optimal protocols for Byzantine agreement. Mathematical Systems Theory, 26(1), pages 41--102, 1993.

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V. Hadzilacos and J. Y. Halpern. Message-optimal protocols for Byzantine agreement. Mathematical Systems Theory, 26(1):41-102, 1993.

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