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arXiv 2008.00332cs.DCcs.CRcs.DS
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多核数据不经意算法

Data Oblivious Algorithms for Multicores

Vijaya Ramachandran, Elaine Shi

摘要:

随着诸如英特尔SGX(具有超线程)等安全处理器的广泛采用,对大数据的私人分析的需求越来越大。大多数数据不经意算法的工作采用经典的PRAM模型来捕获并行性。然而,人们普遍认为PRAM并不能最好地捕捉现实的多核处理器,也不能反映实际中采用的并行编程模型。在本文中,我们开始研究并行数据不经意算法在现实的多核,最好的捕获的二进制fork-join模型的计算。我们首先证明了数据无关排序可以通过具有最佳总工作和最佳(缓存无关)缓存复杂度的二进制fork-join算法来完成,并且在O(log n log log n)跨度(即,并行时间)匹配最著名的不安全算法。使用我们的排序算法作为核心原语,我们展示了如何在二进制fork-join模型中以非平凡的效率模拟一般PRAM算法。我们还提出了几个应用程序,包括列表排名,欧拉之旅,树收缩,连接组件,最小生成森林的结果。对于这些应用程序的一个子集,我们的数据无关算法渐近优于最知名的不安全算法。对于其他应用程序,我们展示了数据不经意的算法,其性能界限匹配最知名的不安全算法。补充这些渐近有效的结果,我们提出了一个实际的变种,我们的排序算法,是独立的和潜在的实现。它具有最佳的缓存成本,它是从最佳的工作和关于一个log n的因素关闭的跨度,而且,它实现了小的常数因子在其边界。

英文摘要:

As secure processors such as Intel SGX (with hyperthreading) become widely adopted, there is a growing appetite for private analytics on big data. Most prior works on data-oblivious algorithms adopt the classical PRAM model to capture parallelism. However, it is widely understood that PRAM does not best capture realistic multicore processors, nor does it reflect parallel programming models adopted in practice. In this paper, we initiate the study of parallel data oblivious algorithms on realistic multicores, best captured by the binary fork-join model of computation. We first show that data-oblivious sorting can be accomplished by a binary fork-join algorithm with optimal total work and optimal (cache-oblivious) cache complexity, and in O(log n log log n) span (i.e., parallel time) that matches the best-known insecure algorithm. Using our sorting algorithm as a core primitive, we show how to data-obliviously simulate general PRAM algorithms in the binary fork-join model with non-trivial efficiency. We also present results for several applications including list ranking, Euler tour, tree contraction, connected components, and minimum spanning forest. For a subset of these applications, our data-oblivious algorithms asymptotically outperform the best known insecure algorithms. For other applications, we show data oblivious algorithms whose performance bounds match the best known insecure algorithms. Complementing these asymptotically efficient results, we present a practical variant of our sorting algorithm that is self-contained and potentially implementable. It has optimal caching cost, and it is only a log log n factor off from optimal work and about a log n factor off in terms of span; moreover, it achieves small constant factors in its bounds.

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