几种高速缓存不经意算法的平衡划分
Balanced Partitioning of Several Cache-Oblivious Algorithms
摘要：
Frigo等人提出了一种理想的缓存模型和递归技术，以缓存无关的方式设计顺序缓存高效算法。Ballard等人指出，将该技术扩展到任意架构是一个基本的开放问题。Ballard等人提出了另一个悬而未决的问题，即如何在任意数量的处理器上准确有效地并行化Strassen算法。我们提出了一种新的方式分区的高速缓存不经意的算法，以实现完美的强缩放任意数量，甚至是素数，在一定范围内的共享内存设置的处理器。我们的方法是处理器感知但缓存不经意（PACO）。我们展示了我们的方法在几个重要的高速缓存无关算法，包括LCS，一维，GAP，经典的矩形矩阵乘法的半环，和Strassen的算法。我们将讨论如何将我们的方法扩展到分布式内存架构，甚至异构计算系统。因此，我们的工作可能会提供一个新的角度上的基本开放的问题，扩展递归缓存无关技术的任意架构。我们提供了一个几乎精确的解决方案，并行化Strassen的开放问题。我们的方法可能会提供一个新的角度扩展递归缓存无关技术的任意架构。我们的所有算法都比最著名的算法表现出更好的可扩展性或更好的总体并行缓存复杂性。初步的实验证明了我们的理论预测，PACO算法可以显着优于最先进的处理器不经意（PO）和处理器感知（PA）的同行。
英文摘要：
Frigo et al. proposed an ideal cache model and a recursive technique to design sequential cache-efficient algorithms in a cache-oblivious fashion. Ballard et al. pointed out that it is a fundamental open problem to extend the technique to an arbitrary architecture. Ballard et al. raised another open question on how to parallelize Strassen's algorithm exactly and efficiently on an arbitrary number of processors. We propose a novel way of partitioning a cache-oblivious algorithm to achieve perfect strong scaling on an arbitrary number, even a prime number, of processors within a certain range in a shared-memory setting. Our approach is Processor-Aware but Cache-Oblivious (PACO). We demonstrate our approach on several important cache-oblivious algorithms, including LCS, 1D, GAP, classic rectangular matrix multiplication on a semiring, and Strassen's algorithm. We discuss how to extend our approach to a distributed-memory architecture, or even a heterogeneous computing system. Hence, our work may provide a new perspective on the fundamental open problem of extending the recursive cache-oblivious technique to an arbitrary architecture. We provide an almost exact solution to the open problem on parallelizing Strassen. Our approach may provide a new perspective on extending the recursive cache-oblivious technique to an arbitrary architecture. All our algorithms demonstrate better scalability or better overall parallel cache complexities than the best known algorithms. Preliminary experiments justify our theoretical prediction that the PACO algorithms can outperform significantly state-of-the-art Processor-Oblivious (PO) and Processor-Aware (PA) counterparts.
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