By Hagit Attiya
* complete creation to the basic ends up in the mathematical foundations of dispensed computing
* observed by way of helping fabric, akin to lecture notes and ideas for chosen exercises
* each one bankruptcy ends with bibliographical notes and a suite of exercises
* Covers the elemental versions, concerns and strategies, and lines many of the extra complex subject matters
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Extra info for Distributed Computing: Fundamentals, Simulations, and Advanced Topics
We then forced the ring into a quiescent con figuration. Finally, we forced H % - 1 ) additional messages to be received from the quiescent configuration, while keeping either ep or e q open. Thus we have con structed an open schedule in which at least 2M ( % ) + � ( % - 1 ) messages are received. 4 SYNCHRONOUS RINGS We now turn to the problem of electing a leader in a synchronous ring. Again, we present both upper and lower bounds. For the upper bound, two leader election alga- SYNCHRONOUS RINGS 43 rithms that require 0 ( n) messages are presented.
Therefore, the message complexity of Algorithm 4 is at most n times the message complexity of Algorithm 3, that is, O ( n m ) . The time complexity is similar to the time complexity of Algorithm 3, that is, O ( m ) . 12 Algorithm 4 finds a spanning tree ofa network with m edges and n nodes, with message complexity 0 ( n m ) and time complexity 0 ( m) . 1 Code one of the simple algorithms in state transitions. 2 when communication is synchronous and when communication is asyn chronous. Hint: For the synchronous case, prove that during round t + 1 , a processor at height t sends a message to its parent.
From the description of the algorithm, (M) is initially in transit to each processor Pi at distance l from Pr . By the definition of time complexity for the asynchronous model, Pi receives (M) by time l . We must show that every processor Pi 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) 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.