Distributed Computing: Fundamentals, Simulations, and by Hagit Attiya

By Hagit Attiya

* complete advent to the basic leads to the mathematical foundations of disbursed computing
* followed by means of aiding fabric, equivalent to lecture notes and suggestions for chosen exercises
* each one bankruptcy ends with bibliographical notes and a suite of exercises
* Covers the basic versions, matters and methods, and contours a few of the extra complex themes

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Additional info for Distributed Computing: Fundamentals, Simulations, and Advanced Topics

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Hint: For the synchronous case, prove that during round t + 1 , a processor at height t sends a message to its parent. For the asynchronous case, prove that by time t, a processor at height t has sent a message to its parent. 2 to collect all the infor­ mation. That is, when the algorithm terminates, the root should have the input values of all the processors. Analyze the bit complexity, that is, the total number of bits that are sent over the communication channels. 6 that a processor is reachable from Pr in G if and only if it ever sets its parent variable.

The basis is t = 1 . From the description of the algorithm, each child of Pr receives (M) from Pr in the first round. We now assume that every processor at distance t - 1 2:: 1 from Pr in the spanning tree receives the message (M) in round t - 1 . We must show that every processor p; at distance t from Pr i n the spanning tree receives (M) in round t. Let Pi be the parent of p; in the spanning tree. Since Pi is at distance t - 1 from Pr . by the inductive hypothesis, Pi receives (M) in round t - 1 .

For the inductive step, assume the lemma holds for round k 1 . Because the processors are in the same state in round k 1 , they all send the same message mr to the right and the same message ml to the left. In round k, every processor receives the message me on its right edge and the message mr on its left edge. Thus all processors receive exactly the same messages in round k; because they execute the 0 same program, they are in the same state at the end of round k. - - The above lemma implies that if at the end of some round some processor an­ nounces itself as a leader, by entering an elected state, so do all other processors.

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