Algorithms And Data Structures

Read e-book online Algorithms of informatics, vol.2.. applications (2007)(ISBN PDF

By Ivanyi A. (ed.)

ISBN-10: 9638759623

ISBN-13: 9789638759627

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

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

Example text

It uses the same data structures as previous Ordered-Bbroadcast. The main dierence between reliable CausallyOrdered-Broadcast and Ordered-Broadcast are as follows: instead of using integer timestamps processors use vector timestamps T , and they do not estimate timestamps of other processors, only compare in lexicographic order their own (vector) timestamps with received ones. The intuition behind vector timestamp of processor pi is that it stores information how many messages have been sent by pi and how many have been accepted by pi from every pk , where k = i.

Moreover the validity condition is clearly satised since the decision value is the input of some processor. It remains to show that the agreement condition holds. 12 In every execution at the end of round f + 1, Vi = Vj , for every two nonfaulty processors pi and pj . Proof We prove the claim by showing that if x ∈ Vi at the end of round f + 1 then x ∈ Vj at the end of round f + 1. Let r be the rst round in which x is added to Vi for any nonfaulty processor pi . If x is initially in Vi let r = 0.

837 n . n−f Communication schedules A local permutation is a permutation of all the integers in the range [0 . n − 1]. We assume that prior the computation there is given set Π of n local permutations. Each processor pi has such a permutation πi from Π. For simplicity we assume that πi (0) = pi . 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.

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


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