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

By Ivanyi A. (ed.)

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Ordered broadcast services We now describe implementations of algorithms for various broadcast services. 620 13. Distributed Algorithms Implementing basic broadcast on top of asynchronous point-to-point messaging The bb service is implemented as follows. If event bc-sendi (m, bb) occurs then processor pi sends message m via every link from pi to pj , where 0 ≤ i ≤ n − 1. If a message m comes to processor pj then it enables event bc-recvj (m, i, bb). To provide reliability we do the following. We build the reliable broadcast on the top of basic broadcast service.

Hence, in order for the value of component i of processor pj to be k or more at the moment y is executed, there must be a chain of instructions and messages that passes a value at least k , originating at processor pi . This chain starts at x or at an instruction executed by pi subsequent to x. But the existence of such chain would imply that x happens before y , which we assumed was not the case. So the component i of vector clock V T (y) is strictly smaller than the component i of vector clock V T (x).

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 . Note that no instruction happens before itself. We write x

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