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.
We consider Oblivious Shuffling and K-Oblivious Shuffling, a refinement thereof. We provide efficient algorithms for both and discuss their application to the design of Oblivious RAM. The task of K-Oblivious Shuffling is to obliviously shuffle N encrypted blocks that have been randomly allocated on the server in such a way that an adversary learns nothing about the new allocation of blocks. The security guarantee should hold also with respect to an adversary that has learned the initial position of K touched blocks out of the N blocks. The classical notion of Oblivious Shuffling is obtained fo…
We present a deterministic sorting algorithm, SPMS (Sample, Partition, and Merge Sort), that interleaves the partitioning of a sample sort with merging. Sequentially, it sorts $n$ elements in $O(n \log n)$ time cache-obliviously with an optimal number of cache misses. The parallel complexity (or critical path length) of the algorithm is $O(\log n \cdot \log\log n)$, which improves on previous bounds for optimal cache oblivious sorting. The algorithm also has low false sharing costs. When scheduled by a work-stealing scheduler in a multicore computing environment with a global shared memory and…
PACO: A Fully Cache-Oblivious Parallel FFT with One Global Redistribution
College of Computer Science and Artificial Intelligence, Fudan University（复旦大学计算机科学与人工智能学院）；School of Mathematical Sciences, School of Data Science, Fudan University（复旦大学数学科学学院、数据科学学部）；Shanghai Key Lab. of Intelligent Information Processing（上海市智能信息处理重点实验室）
Classic cache-oblivious parallel matrix multiplication algorithms achieve optimality either in time or space, but not both, which promotes lots of research on the best possible balance or tradeoff of such algorithms. We study modern processor-oblivious runtime systems and figure out several ways to improve algorithm's time bound while still bounding space and cache requirements to be asymptotically optimal. By our study, we give out sublinear time, optimal work, space and cache algorithms for both general matrix multiplication on a semiring and Strassen-like fast algorithm. Our experiments als…
Multi-core processors improve performance, but they can create unpredictability owing to shared resources such as caches interfering. Cache partitioning is used to alleviate the Worst-Case Execution Time (WCET) estimation by isolating the shared cache across each thread to reduce interference. It does, however, prohibit data from being transferred between parallel threads running on different cores. In this paper we present (SRCP) a cache replacement mechanism for partitioned caches that is aware of data being shared across threads, prevents shared data from being replicated across partitions …
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-ob…
The nested parallel (a.k.a. fork-join) model is widely used for writing parallel programs. However, the two composition constructs, i.e. "$\parallel$" (parallel) and "$;$" (serial), are insufficient in expressing "partial dependencies" or "partial parallelism" in a program. We propose a new dataflow composition construct "$\leadsto$" to express partial dependencies in algorithms in a processor- and cache-oblivious way, thus extending the Nested Parallel (NP) model to the \emph{Nested Dataflow} (ND) model. We redesign several divide-and-conquer algorithms ranging from dense linear algebra to dy…
Accelerating State-Vector Quantum Simulation on Integrated GPUs via Cache Locality Optimization: A Cross-Architecture Evaluation
Instituto de Pesquisas Eldorado（Eldorado研究所）；Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学）；Pontifícia Universidade Católica do Rio Grande do Sul（南里奥格兰德天主教 Pontifícia 大学）
