By Ivanyi A. (ed.)

ISBN-10: 9638759623

ISBN-13: 9789638759627

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5. Logical time, causality, and consistent state 617 Snapshot avoids this cost. In the algorithm, a processor initiates the calculation of consistent cut by ooding the network with a special message that acts like a sword that cuts the execution of algorithm A consistently. In order to prove that the cut is indeed consistent, we require that messages are received by the recipient in the order they were sent by the sender. Such ordering can be implemented using sequence number. In the Distributed-Snapshot algorithm, each processor pi has a variable called counter that counts the number of instructions of algorithm A executed by the processor so far.

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. , sending messages over the (almost) complete binary tree, and then time complexity is O(lg n), while the message complexity is O(n lg n).

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

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