技术报告：在分散式网络超级计算中处理不可靠的工作人员
Technical Report: Dealing with Undependable Workers in Decentralized Network Supercomputing
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。本文提出了一种新的算法，使用网络超级计算来执行大量的独立任务，同时处理不可靠的处理器的问题。对手可以使处理器返回具有某些概率的任务的虚假结果，并且可以使初始处理器集合$P$的子集$F$崩溃。对手在两个方面受到限制。首先，对于未崩溃处理器集合$P-F$，处理器返回假结果的\emph{average}概率低于$\frac{1}{2}$。第二，如果$P-F$的大小从下到上有界，攻击者可能会使处理器$F$的子集崩溃。我们考虑两种模式：第一界的$P-F$的大小由一个分数多项式，第二界这个大小由一个多对数。这两种模型产生的对手比以前研究的要强大得多。我们的随机同步算法制定$n$处理器和$t$任务，与$n\le t$，其中取决于崩溃的数量，每个活的处理器能够动态终止的知识，问题得到解决的概率很高。对于分数阶多项式约束的攻击者，算法的轮复杂度为$O(\frac{t}{n^\varepsilon}\log{n}\log{\log{n}})$，其工作复杂度为$O(t\log{n} \log{\log{n}})$，消息复杂度为$O(n\log{n}\log{\log{n}})$ .对于多对数约束攻击者，轮复杂度为$O(t)$，功为$O(t n^{\varepsilon})$，% $O(t \, poly \log{n})$，消息复杂度为$O(n^{1+\varepsilon})$ % $O(n \, poly \log{n})$。所有的界限都显示持有高概率。
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. This paper presents a new algorithm for the problem of using network supercomputing to perform a large collection of independent tasks, while dealing with undependable processors. The adversary may cause the processors to return bogus results for tasks with certain probabilities, and may cause a subset $F$ of the initial set of processors $P$ to crash. The adversary is constrained in two ways. First, for the set of non-crashed processors $P-F$, the \emph{average} probability of a processor returning a bogus result is inferior to $\frac{1}{2}$. Second, the adversary may crash a subset of processors $F$, provided the size of $P-F$ is bounded from below. We consider two models: the first bounds the size of $P-F$ by a fractional polynomial, the second bounds this size by a poly-logarithm. Both models yield adversaries that are much stronger than previously studied. Our randomized synchronous algorithm is formulated for $n$ processors and $t$ tasks, with $n\le t$, where depending on the number of crashes each live processor is able to terminate dynamically with the knowledge that the problem is solved with high probability. For the adversary constrained by a fractional polynomial, the round complexity of the algorithm is $O(\frac{t}{n^\varepsilon}\log{n}\log{\log{n}})$, its work is $O(t\log{n} \log{\log{n}})$ and message complexity is $O(n\log{n}\log{\log{n}})$. For the poly-log constrained adversary, the round complexity is $O(t)$, work is $O(t n^{\varepsilon})$, %$O(t \, poly \log{n})$, and message complexity is $O(n^{1+\varepsilon})$ %$O(n \, poly \log{n})$. All bounds are shown to hold with high probability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
