文章基本信息

标题：Sample-And-Gather: Fast Ruling Set Algorithms in the Low-Memory MPC Model
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作者：Kishore Kothapalli ; Shreyas Pai ; Sriram V. Pemmaraju 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：182
页码：1-18
DOI：10.4230/LIPIcs.FSTTCS.2020.28
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Motivated by recent progress on symmetry breaking problems such as maximal independent set (MIS) and maximal matching in the low-memory Massively Parallel Computation (MPC) model (e.g., Behnezhad et al. PODC 2019; Ghaffari-Uitto SODA 2019), we investigate the complexity of ruling set problems in this model. The MPC model has become very popular as a model for large-scale distributed computing and it comes with the constraint that the memory-per-machine is strongly sublinear in the input size. For graph problems, extremely fast MPC algorithms have been designed assuming Î©Ìf(n) memory-per-machine, where n is the number of nodes in the graph (e.g., the O(log log n) MIS algorithm of Ghaffari et al., PODC 2018). However, it has proven much more difficult to design fast MPC algorithms for graph problems in the low-memory MPC model, where the memory-per-machine is restricted to being strongly sublinear in the number of nodes, i.e., O(n^Îµ) for constant 0 1. Specifically, we show that a Î²-ruling set can be computed in the low-memory MPC model with O(n^Îµ) memory-per-machine in OÌf(Î² â 1, these algorithms are all substantially faster than the Ghaffari-Uitto OÌf(â^S{log Î"})-round MIS algorithm in the low-memory MPC model. All our results follow from a Sample-and-Gather Simulation Theorem that shows how random-sampling-based Congest algorithms can be efficiently simulated in the low-memory MPC model. We expect this simulation theorem to be of independent interest beyond the ruling set algorithms derived here.
关键词：Massively Parallel Computation; Ruling Set; Simulation Theorems