By Ivanyi A. (ed.)
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Mt−1 are the messages such that events bc-recvj (< m0 , 0 >, i, bb),. . ,bc-recvj (< mt−1 , t− 1 >, i, bb) have been enabled. Note that if we use reliable Basic Broadcast instead of Basic Broadcast as the background service, the above implementation of Single-Source FIFO becomes Reliable Single-Source FIFO service. We leave the proof to the reader as an exercise. Implementing causal order and total order on the top of single-source We present an ordered broadcast algorithm which works in the FIFO service.
Kn ) that processors collectively find turns out to be a consistent cut. 24 For any cut K, the cut K computed by the Consistent-Cut algorithm is a consistent cut majorised by K. Proof First observe that there is no need to consider entries of V Ti further than ki . Each of these entries is not majorised by K, because the i-th coordinate of any of these vectors is strictly larger than ki . So we can indeed focus on searching among the first ki entries of V Ti . Let ki ≥ 0 be the largest entry such that the vector V Ti [ki ] is majorised by the vector K.
The Vector-Clocks algorithm allows processors to relate instructions, and this relation is exactly the happens before relation. Each processor pi maintains a vector Vi of n integers. The j-th coordinate of the vector is denoted by Vi [j]. The vector is initialised to the zero vector (0, . . , 0). A vector is modified each time processor executes an instruction, in a way similar to the way counter was modified in the Logical-Clock algorithm. Specifically, when a processor pi executes any instruction other than sending or receiving a message, the coordinate Vi [i] gets incremented by one, and other coordinates remain intact.