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

By Ivanyi A. (ed.)

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Extra info for Algorithms of informatics, vol. 2

Example text

In this kind of communication processor pi considers the processors as ordered by its local permutation πi , that is, in the order πi (0), πi (1), . . , πi (n − 1). Some of additional messages sent in this process are called range ones. During regular phase processors send the following kind of range messages: inquiring, reply and notifying messages. A collector pi sends an inquiring message to the first processor about which pi has not heard yet. Each recipient of such a message sends back a range message that is called a reply one.

We argue that (k1 , . . , kn ) is a consistent cut by way of contradiction. Suppose that the vector (k1 , . . , kn ) is an inconsistent cut. Then, by definition, there are processors pi and pj such that there is an instruction x of processor pi subsequent to 618 13. Distributed Algorithms instruction number ki , such that x happens before instruction number kj of processor pj . Recall that ki is the furthest entry of V Ti majorised by K. 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.

Processor executes instructions, and stores vector timestamps in consecutive entries of the table. Specifically, entry m of the table is the vector timestamp V Ti [m] of the mth instruction executed by the processor; we define V Ti [0] to be the zero vector. Processor pi begins calculating a cut right after the moment when the processor has executed instruction number ki . The processor determines the largest number ki ≥ 0 that is at most ki , such that the vector V Ti [ki ] is majorised by K. The vector K = (k1 , .

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