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By Ivanyi A. (ed.)

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Extra info for Algorithms of informatics, vol. 2

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Communication services Among the fundamental problems in distributed systems where processors communicate by message passing are the tasks of spreading and gathering information. Many distributed algorithms for communication networks can be constructed using building blocks that implement various broadcast and multicast services. In this section we present some basic communication services in the message-passing model. Such services typically need to satisfy some quality of service requirements dealing with ordering of messages and reliability.

Notice that processor pi has heard about processor pj , if one among the values Rumorsi [j] and Activei [j] is not equal to nil. The purpose of using the array Pending is to facilitate dissemination. Each time processor pi learns that some other processor pj is fully informed, that is, it is either a disseminator itself or has been notified by a disseminator, then it marks this information in Pendingi [j]. Processor pi uses the array Pendingi to send dissemination messages in a systematic way, by scanning Pendingi to find those processors that possibly still have not heard about some processor.

16 they will decide on the same value at the end of the algorithm. Hence the algorithm has the agreement property and solves consensus. 18 There exists an algorithm for n processors which solves the consensus problem in the presence of f Byzantine failures within 2(f + 1) rounds using constant size messages, if n > 4f . 6. Impossibility in asynchronous systems As shown before, the consensus problem can be solved in synchronous systems in the presence of both crash (benign) and Byzantine (severe) failures.

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