From WAB Oracles to Atomic Broadcast Sample Clauses

From WAB Oracles to Atomic Broadcast. (Version 1) In this section we give a simple version of our atomic broadcast algorithm; in the next section we extend it to include some optimizations.
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From WAB Oracles to Atomic Broadcast. Version 1 In this section we give a simple version of our atomic broadcast algorithm; we extend it in Section 4.4 with some optimizations. − Overview of the algorithm. The structure of our atomic broadcast algorithm is close to the structure of the R-Consensus algorithm (Section 3.3) and also assumes f < n/3. The main difference is that the atomic broadcast algorithm uses sequences of messages instead of single messages. The execution proceeds in rounds; to broadcast a message, process p concatenates the message with a sequence that it keeps locally, denoted estimate. Processes send their estimate sequence to other processes in the first stage of a round using the WAB oracle, and wait for the first sequence, with the current round number, output by the oracle. In the second stage, processes exchange the estimate sequences output by the oracle in the first stage (possiblywith some other messages appended). Each process waits for n f messages. If all sequences received have a common non- empty prefix, the process A-delivers the messages in the common prefix not yet A-delivered. Then, the process determines the longest prefix among a majority of the sequences received; this prefix, followed byany other messages the process mayhave received, is the process’ new estimate. The process then starts the next round. The algorithm in detail. Algorithm 3, page 55, is the first version of our atomic broadcast algorithm. Tasks 1, 2 and 3 execute concurrently. Variable rp (line 2) is the current round number, estimatep (line 3) contains a sequence of messages broadcast by p or byanyother process, and deliveredp (line 4) contains the se- quence of messages A-delivered by p, in the order in which theywere A-delivered. To broadcast a message m, process p appends m to estimatep (line 6, Task 1). The main algorithm and actual broadcasting of messages is performed byTask 2 (lines 8–20). Task 3 (lines 21–22) ensures the validitypropertyof atomic broad- cast. The variable estimatep is concurrently accessed by Task 1, Task 2, and Task 3; we implicitly assume that it is accessed in mutual exclusion (e.g., using semaphores). The proof of the algorithm is given in [17]. Correctness follows from the following invariants. Let p and q be two processes: – If p terminates round r and q is correct, then q terminates round r. – If p and q terminate round r, either deliveredr is a prefix of deliveredr or p q deliveredr is a prefix of deliveredr. q p – If p executes round r until the end, an...
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