技术报告：协同分布式计算中工作者可靠性的评估
Technical Report: Estimating Reliability of Workers for Cooperative Distributed Computing
摘要：
互联网超级计算是一种通过利用大量互连计算机的能力来解决可划分的计算密集型问题的方法。对于使用网络超级计算来执行大量独立任务的问题，先前的工作引入了一种分散的方法，并提供了随机同步算法，该算法以高概率正确执行所有任务，同时处理行为不端或易崩溃的处理器。现有算法的主要弱点是它们假设未崩溃处理器返回不正确结果的\emph{average}概率低于$\frac{1}{2}$，或者返回不正确结果的概率对于\emph{each}处理器是已知的。在这里，我们提出了一个随机化的同步分布式算法，紧密估计每个处理器返回正确结果的概率。从$n$处理器的集合$P$开始，让$F$成为崩溃的处理器集合。我们的算法估计概率$p_i$返回一个正确的结果，为每个处理器$i \in P-F$，使所有这些处理器的估计。估计基于$(ε, δ)$近似，其中对于用户选择的任何常数$δ>0$和$ε>0$，$p_i$的每个估计概率$\tilde{p_i}$服从界限${\sf Pr}[p_i(1-ε) \leq \tilde{p_i} \leq p_i(1+ε)] > 1 - δ$。该算法的一个重要方面是，每个处理器终止没有全局协调。我们评估了算法在三个对抗模型中的效率，如下所示。对于其中未崩溃处理器的数目$|P-F|$是线性有界的模型，算法的时间复杂度$T(n)$是$Θ(\log{n})$，工作复杂度$W(n)$是$Θ(n\log{n})$，并且消息复杂度$M(n)$是$Θ(n\log^2n)$。
英文摘要：
Internet supercomputing is an approach to solving partitionable, computation-intensive problems by harnessing the power of a vast number of interconnected computers. For the problem of using network supercomputing to perform a large collection of independent tasks, prior work introduced a decentralized approach and provided randomized synchronous algorithms that perform all tasks correctly with high probability, while dealing with misbehaving or crash-prone processors. The main weaknesses of existing algorithms is that they assume either that the \emph{average} probability of a non-crashed processor returning incorrect results is inferior to $\frac{1}{2}$, or that the probability of returning incorrect results is known to \emph{each} processor. Here we present a randomized synchronous distributed algorithm that tightly estimates the probability of each processor returning correct results. Starting with the set $P$ of $n$ processors, let $F$ be the set of processors that crash. Our algorithm estimates the probability $p_i$ of returning a correct result for each processor $i \in P-F$, making the estimates available to all these processors. The estimation is based on the $(ε, δ)$-approximation, where each estimated probability $\tilde{p_i}$ of $p_i$ obeys the bound ${\sf Pr}[p_i(1-ε) \leq \tilde{p_i} \leq p_i(1+ε)] > 1 - δ$, for any constants $δ>0$ and $ε>0$ chosen by the user. An important aspect of this algorithm is that each processor terminates without global coordination. We assess the efficiency of the algorithm in three adversarial models as follows. For the model where the number of non-crashed processors $|P-F|$ is linearly bounded the time complexity $T(n)$ of the algorithm is $Θ(\log{n})$, work complexity $W(n)$ is $Θ(n\log{n})$, and message complexity $M(n)$ is $Θ(n\log^2n)$.
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