Efficient massively parallel methods for dynamic programming

Sungjin Im, Benjamin Moseley, Xiaorui Sun
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引用次数: 53

Abstract

Modern science and engineering is driven by massively large data sets and its advance heavily relies on massively parallel computing platforms such as Spark, MapReduce, and Hadoop. Theoretical models have been proposed to understand the power and limitations of such platforms. Recent study of developed theoretical models has led to the discovery of new algorithms that are fast and efficient in both theory and practice, thereby beginning to unlock their underlying power. Given recent promising results, the area has turned its focus on discovering widely applicable algorithmic techniques for solving problems efficiently. In this paper we make progress towards this goal by giving a principled framework for simulating sequential dynamic programs in the distributed setting. In particular, we identify two key properties, monotonicity and decomposability, which allow us to derive efficient distributed algorithms for problems possessing the properties. We showcase our framework by considering several core dynamic programming applications, Longest Increasing Subsequence, Optimal Binary Search Tree, and Weighted Interval Selection. For these problems, we derive algorithms yielding solutions that are arbitrarily close to the optimum, using O(1) rounds and Õ(n/m) memory on each machine where n is the input size and m is the number of machines available.
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高效的大规模并行动态规划方法
现代科学和工程是由海量数据集驱动的,它的进步很大程度上依赖于大规模并行计算平台,如Spark、MapReduce和Hadoop。已经提出了理论模型来理解这些平台的力量和局限性。最近对已开发的理论模型的研究导致了在理论和实践中都快速有效的新算法的发现,从而开始释放其潜在的力量。鉴于最近有希望的结果,该领域已将重点转向发现广泛适用的算法技术,以有效地解决问题。在本文中,我们通过给出一个有原则的框架来模拟分布式环境下的顺序动态程序,从而在这一目标上取得了进展。特别是,我们确定了两个关键性质,单调性和可分解性,这使我们能够为具有这些性质的问题推导出有效的分布式算法。我们通过考虑几个核心动态规划应用,最长递增子序列,最优二叉搜索树和加权区间选择来展示我们的框架。对于这些问题,我们推导出算法,生成任意接近最优的解决方案,在每台机器上使用O(1)轮和Õ(n/m)内存,其中n是输入大小,m是可用机器的数量。
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