In the era of big data and cloud computing, large amounts of data are generated from user applications and need to be processed in the datacenter. Data-parallel computing frameworks, such as Apache Spark, are widely used to perform such data processing at scale. Specifically, Spark leverages distributed memory to cache the intermediate results, represented as Resilient Distributed Datasets (RDDs). This gives Spark an advantage over other parallel frameworks for implementations of iterative machine learning and data mining algorithms, by avoiding repeated computation or hard disk accesses to retrieve RDDs. By default, caching decisions are left at the programmer’s discretion, and the LRU policy is used for evicting RDDs when the cache is full. However, when the objective is to minimize total work, LRU is woefully inadequate, leading to arbitrarily suboptimal caching decisions. In this paper, we design an algorithm for multi-stage big data processing platforms to adaptively determine and cache the most valuable intermediate datasets that can be reused in the future. Our solution automates the decision of which RDDs to cache: this amounts to identifying nodes in a direct acyclic graph (DAG) representing computations whose outputs should persist in the memory. Our experiment results show that our proposed cachemore »
Fast Stencil Computations using Fast Fourier Transforms
Stencil computations are widely used to simulate the change of state of physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping algorithms, cache-oblivious divide-and-conquer trapezoidal algorithms, and Krylov subspace methods.
In this paper, we present two efficient parallel algorithms for performing linear stencil computations. Current direct solvers in this domain are computationally inefficient, and Krylov methods require manual labor and mathematical training. We solve these problems for linear stencils by using DFT preconditioning on a Krylov method to achieve a direct solver which is both fast and general. Indeed, while all currently available algorithms for solving general linear stencils perform Θ(NT) work, where N is the size of the spatial grid and T is the number of timesteps, our algorithms perform o(NT) work.
To the best of our knowledge, we give the first algorithms that use fast Fourier transforms to compute final grid data by evolving the initial data for many timesteps at once. Our algorithms handle both periodic and aperiodic boundary conditions, and achieve polynomially better performance bounds (i.e., computational complexity and parallel runtime) than all other existing solutions.
Initial experimental results show that implementations of our algorithms that more »
- Publication Date:
- NSF-PAR ID:
- 10298518
- Journal Name:
- Annual ACM Symposium on Parallelism in Algorithms and Architectures
- ISSN:
- 1548-6109
- Sponsoring Org:
- National Science Foundation
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