Algorithms of informatics. Applications by Ivanyi A. (ed.)

By Ivanyi A. (ed.)

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The algorithms presented deal with the so called consensus problem , rst introduced by Lamport, Pease, and Shostak. The consensus problem is a fundamental coordination problem that requires processors to agree on a common output, based on their possibly conicting inputs. 1. The consensus problem We consider a system in which each processor pi has a special state component xi , called the input and yi , called the output (also called the decision ). The variable xi initially holds a value from some well ordered set of possible inputs and yi is undened.

Each round consists of the delivery of all messages, followed by one computation event for every processor. The set of faulty processors can be dierent in dierent executions, that is, it is not known in advance. Let F be a subset of at most f processors, the faulty processors. Each round contains exactly one computation event for the processors not in F and at most one computation event for every processor in F . Moreover, if a processor in F does not have a computation event in some round, it does not have such an event in any further round.

Timestamps are used to mark messages before sendingif pi is going to broadcast a message, it increases its timestamp and uses it to tag this message (lines 11-13). 6. Communication services 621 tamp of pj ), it puts t into T [j] (lines 2332). Processor pi sets its current timestamp to be the maximum of the estimated timestamps in the vector T plus one (lines 2426). After updating the timestamp processor sends an update message. Processor accepts a message m with associated timestamp t from processor j if pair (t, j) is the smallest among other received messages (line 42), and each processor has at least as large a timestamp as known by processor pi (line 43).

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