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Ivanyi A. (ed.) Algorithms of informatics, vol.2.. purposes (2007)(ISBN 9638759623)

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Extra info for Algorithms of informatics, vol.2.. applications (2007)(ISBN 9638759623)

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However, if the underlying communication network is prone to failures of components, then irregular failure patterns disturb a ow of information and make gossiping last longer. The question we address in this section is what is the best trade-o between time and message complexity in the model with processor crashes? 2. Ecient gossip algorithms In this part we describe the family of gossip algorithms, among which we can nd some ecient ones. They are all based on the same generic code, and their eciency depends on the quality of two data structures put in the generic algorithm.

Proof Since all nonfaulty processors prefer v at the beginning of phase k, they all receive at least n − f copies of v (including their own) in the rst round of phase k . Since n > 4f , n − f > n/2 + f , implying that all nonfaulty processors will prefer v at the end of phase k . Consensus-with-Byzantine-failures 1 2 3 4 Code for processor pi , 0 ≤ i ≤ n − 1. Initially pref[j] = v⊥ , for any j = i round 2k − 1, 1 ≤ k ≤ f + 1 send pref[i] to all processors receive vj from pj and assign to pref[j], for all 0 ≤ j ≤ n − 1, j = i let maj be the majority value of pref[0],.

When x and y are executed by two dierent processors, then we say that x happens before y if and only if there is a chain of instructions and messages snd1 rcv2 . . snd2 .. rcvk−1 . . sndk−1 rcvk 13. Distributed Algorithms 614 for k ≥ 2, such that snd1 is either equal to x or is executed after x by the same processor that executes x; rcvk is either equal to y or is executed before y by the same processor that executes y ; rcvh is executed before sndh by the same processor, 2 ≤ h < k ; and sndh sends a message that is received by rcvh+1 , 1 ≤ h < k .

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