Do-all computing in distributed systems by C Georgiou; Alex Allister Shvartsman

By C Georgiou; Alex Allister Shvartsman

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J 2 . , j−1, is the double of the number of processors in layer Λi . Layer Λj may contain less processors. When Λ0 = q1 the local view can be visualized as a binary tree rooted at processor q1 , where nodes are placed from left to right with respect to the linear order given by Lw . Thus, in a tree-like local view, layer Λ0 consists of processor q1 , layer Λi consists of 2i consecutive processors starting at processor q2i and ending at processor q2i+1 −1 , with the exception of the very last layer that may contain a smaller number of processors.

Once a processor is crashed, it does not restart. Consider an algorithm A that performs a computation in the presence of adversary AC . Let ξ be an execution in E(A, AC ). We represent the adversarial pattern ξ|AC as a set of triples (crash, pid, t), where crash is the event caused by the adversary, pid is the identifier of the processor that crashes, and t is the time of the execution (according to some external global clock not available to the processors) when the adversary crashes processor pid.

Also, any lower bound developed under the assumption of perfect knowledge, applies equally well to other models where means of communication between processors are specified, for example, message-passing and shared-memory models. 1 Modeling Knowledge Knowledge is modeled via Oracle O that provides termination and loadbalancing information to the processors. In particular, the oracle informs the processors whether the computation is completed and if not, what task to perform next. We assume that the oracle performs perfect load-balancing, that is, the live processors are only allocated to unperformed tasks, and all such tasks are allocated a balanced number of live processors.

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