Distributed Computing: Fundamentals, Simulations, and by Hagit Attiya

By Hagit Attiya

* entire advent to the elemental leads to the mathematical foundations of allotted computing
* followed by way of aiding fabric, similar to lecture notes and recommendations for chosen exercises
* every one bankruptcy ends with bibliographical notes and a suite of exercises
* Covers the basic types, matters and methods, and contours the various extra complex issues

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

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To build a spanning tree, each processor that wakes up spontaneously attempts to build a DFS tree with itself as the root, using a separate copy of Algorithm 3. If two DFS trees try to connect to the same node (not necessarily at the same time), the node will join the DFS tree whose root has the higher identifier. The pseudocode appears in Algorithm 4. To implement the above idea, each node keeps the maximal identifier it has seen so far in a variable leader, which is initialized to a value smaller than any identifier.

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) by time t 1 . B y the description of the algorithm, Pj sends (M) to Pi when i t receives (M), that is, by time t 1. By the definition of time complexity for the asynchronous model, Pi D receives (M) by time t. 4 There is an asynchronous broadcast algorithm with message complex­ ity n 1 and time complexity d, when a rooted spanning tree with depth d is known in advance.

Proof. The proof is by induction on k. The base case, k = 0 (before the first round), is straightforward because the processors begin in the same initial state. 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.

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