O(m log2n)工作和低深度的平行最小切口

IF 0.9 Q3 COMPUTER SCIENCE, THEORY & METHODS ACM Transactions on Parallel Computing Pub Date : 2022-12-16 DOI:10.1145/3565557
Daniel Anderson, G. Blelloch
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引用次数: 3

摘要

我们提出了一种用于最小割的O(m log2n)工作,O(polylogn)深度并行算法。该算法与Gawrychowski、Mozes和Weimann最近的序列算法[ICALP'20]的工作边界相匹配,并改进了Geissmann和Gianinazzi之前的最佳并行算法[SPA'18],该算法在O(polylogn)深度中执行O(m log4n)功。我们的算法使用了三个可能独立感兴趣的组件。首先,我们设计了一个并行数据结构,它有效地支持对树的批量混合查询和更新。它推广和改进了Geissmann和Gianinazzi先前数据结构的工作边界,并且相对于最佳序列算法是有效的。其次,我们设计了一个近似最小割的并行算法,该算法改进了Karger和Motwani先前的结果。我们使用这个算法来给出一个高效的生成树包装的过程,就像Karger的最小切割序列算法一样。最后,我们设计了一个有效的并行算法来解决最小2相关割问题。
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Parallel Minimum Cuts in O(m log2 n) Work and Low Depth
We present a randomized O(m log2 n) work, O(polylog n) depth parallel algorithm for minimum cut. This algorithm matches the work bounds of a recent sequential algorithm by Gawrychowski, Mozes, and Weimann [ICALP’20], and improves on the previously best parallel algorithm by Geissmann and Gianinazzi [SPAA’18], which performs O(m log4 n) work in O(polylog n) depth. Our algorithm makes use of three components that might be of independent interest. Firstly, we design a parallel data structure that efficiently supports batched mixed queries and updates on trees. It generalizes and improves the work bounds of a previous data structure of Geissmann and Gianinazzi and is work efficient with respect to the best sequential algorithm. Secondly, we design a parallel algorithm for approximate minimum cut that improves on previous results by Karger and Motwani. We use this algorithm to give a work-efficient procedure to produce a tree packing, as in Karger’s sequential algorithm for minimum cuts. Lastly, we design an efficient parallel algorithm for solving the minimum 2-respecting cut problem.
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来源期刊
ACM Transactions on Parallel Computing
ACM Transactions on Parallel Computing COMPUTER SCIENCE, THEORY & METHODS-
CiteScore
4.10
自引率
0.00%
发文量
16
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