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By Ivanyi A. (ed.)

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Additional info for Algorithms of informatics, vol. 2

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Then condition in line 42 guarantees acceptance in order of (t, k), (t , l). Case 2. Triple (m, t, k) (without loss of generality) is accepted by processor pi before triple (m , t , l) is pending. If (t, k) < (t , l) then still the acceptance is according to the order of (t, k), (t , l). Otherwise (t, k) > (t , l), and by condition in line 43 we get in particular that t ≤ T [l], and consequently t ≤ T [l]. This can not happen because of the ssf requirement and the assumption that processor pi has not yet received message < m , t > from l via the ssf broadcast service.

When an event bcrecvj (< m, D >, i, qos) occurs, processor pj enables event mc-recvj (m, i, qos) if pj ∈ D, otherwise it ignores this event. The proof that such method provides required multicast quality of service is left as an exercise. 7. Rumor collection algorithms Reliable multicast services can be used as building blocks in constructing algorithms for more advanced communication problems. In this section we illustrate this method for the problem of collecting rumors by synchronous processors prone to crashes.

Communication services 621 Integrity: each message m received in event bc-recv has been sent in some bc-send event. No-Duplicates: each processor receives a message not more than once. Liveness: each message sent is received by all processors. In the model with failures we define the notion of reliable broadcast service, which satisfies Integrity, No-Duplicates and two kinds of Liveness properties: Nonfaulty Liveness: each message m sent by non-faulty processor pi must be received by every non-faulty processor.

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