Algorithms of informatics. Applications by Ivanyi A. (ed.)

By Ivanyi A. (ed.)

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Local permutation is used to collect rumor in systematic way according to the order given by this permutation, while communication graphs are rather used to exchange already collected rumors within large and compact non-faulty graph component. Generic algorithm We start with specifying a goal that gossiping algorithms need to achieve. 7. Rumor collection algorithms 627 that processor pi has heard about processor pj if either pi knows the original input rumor of pj or p knows that pj has already failed.

Consensus-with-Crash-Failures 1 2 3 4 5 Code for processor pi , 0 ≤ i ≤ n − 1. Initially V = {x} round k , 1 ≤ k ≤ f + 1 send {v ∈ V : pi has not already sent v} to all processors receive Sj from pj , 0 ≤ j ≤ n − 1, j = i n−1 V ← V ∪ j=0 Sj if k = f + 1 then y ← min(V ) In the previous algorithm, which is based on an algorithm by Dolev and Strong, each processor maintains a set of the values it knows to exist in the system. Initially, the set contains only its own input. In later rounds the processor updates its set by joining it with the sets received from other processors.

The following simple algorithm completes gossip in just one synchronous step: each processor broadcasts its rumor to all processors. The algorithm is correct, because each message received contains a rumor, and a message not received means the failure of its sender. A drawback of such a solution is that a quadratic number of messages could be sent, which is quite inecient. We would like to perform gossip not only quickly, but also with fewer point-topoint messages. There is a natural trade-o between time and communication.

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