Algorithms of informatics, vol. 2 by Ivanyi A. (ed.)

By Ivanyi A. (ed.)

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Extra info for Algorithms of informatics, vol. 2

Example text

Sndk−1 rcvk 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

So entry ki + 1 is not majorised by K, and since all subsequent entries, including the one for instruction x, can have only larger coordinates, the entries are not majorised by K either. But, x happens before instruction number kj , so entry kj can only have lager coordinates than respective coordinates of the entry corresponding to x, and so V Tj [kj ] cannot be majorised by K either. This contradicts the assumption that V Tj [kj ] is majorised by K. Therefore, (k1 , . . , kn ) must be a consistent cut.

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 inefficient. We would like to perform gossip not only quickly, but also with fewer point-topoint messages. There is a natural trade-off between time and communication.

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