Acknowledgments: 5.2 Lower Bound for General Algorithms

Lower and upper bounds are proved for the time complexity of solving two decision problems in a distributed network in the presence of process failures and inexact information about time. It is assumed that the amount of (real) time between two consecutive steps of a nonfaulty process is at least c1 and at most c2; thus, C = c2=c1 is a measure of the timing uncertainty. It is also assumed that a message sent by a nonfaulty process is delivered within time at most d. Processes fail by not obeying the timing requirements on their steps and on messages they send (late timing failures). This paper presents a new stretching technique for deriving lower bounds in this model in the presence of timing failures. The combination of this technique with known bounds yields two new lower bounds for this model: 1. Any comparison-based renaming algorithm has a worst-case running time of (logn Cd), in the presence of n 1 timing failures. 2. Any agreement algorithm has a worst-case running time of ( n n fCd), in the presence of f timing failures, for any f n=2. The paper also presents a general transformation in the presence of late timing failures. The transformation turns an r-round synchronous algorithm into a semi-synchronous algorithm with worst case time O(r Cd). Time Bounds for Decision Problems in the Presence of Timing Uncertainty and Failures1 Hagit Attiya and Taly Djerassi-Shintel Computer Science Department The Technion Haifa 32000 Israel November 9, 1994 1A preliminary version of this paper appeared in proceedings of the 7th International Workshop on Distributed Algorithms 1993, (A. Schiper, Ed.), 204{218, Lecture Notes in Computer Science #725, Springer-Verlag. This work was supported by grant No. 92-0233 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel, and the fund for the promotion of research in the Technion.