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Parallel Peeling Algorithms

Authors:

Michael Mitzenmacher,

Justin ThalerAuthors Info & Claims

ACM Transactions on Parallel Computing (TOPC), Volume 3, Issue 1

Article No.: 7, Pages 1 - 27

https://doi.org/10.1145/2938412

Published: 16 January 2017 Publication History

Abstract

The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k are removed until there are no vertices of degree less than k left. The remaining hypergraph is known as the k-core. In this article, we analyze parallel peeling processes, in which in each round, all vertices of degree less than k are removed. It is known that, below a specific edge-density threshold, the k-core is empty with high probability. We show that, with high probability, below this threshold, only 1/log((k-1)(r-1)) log log n + O(1) rounds of peeling are needed to obtain the empty k-core for r-uniform hypergraphs. This bound is tight up to an additive constant. Interestingly, we show that, above this threshold, Ω(log n) rounds of peeling are required to find the nonempty k-core. Since most algorithms and data structures aim to peel to an empty k-core, this asymmetry appears fortunate. We verify the theoretical results both with simulation and with a parallel implementation using graphics processing units (GPUs). Our implementation provides insights into how to structure parallel peeling algorithms for efficiency in practice.

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Cited By

Arafat NKhan ARai AGhosh B(2023)Neighborhood-Based Hypergraph Core DecompositionProceedings of the VLDB Endowment10.14778/3598581.359858216:9(2061-2074)Online publication date: 1-May-2023
https://dl.acm.org/doi/10.14778/3598581.3598582
Choe MKim SYoo JShin KSingh ASun YAkoglu LGunopulos DYan XKumar ROzcan FYe J(2023)Classification of Edge-dependent Labels of Nodes in HypergraphsProceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3580305.3599274(298-309)Online publication date: 6-Aug-2023
https://dl.acm.org/doi/10.1145/3580305.3599274
Luo QYu DLiu YZheng YCheng XLin X(2023)Finer-Grained Engagement in Hypergraphs2023 IEEE 39th International Conference on Data Engineering (ICDE)10.1109/ICDE55515.2023.00039(423-435)Online publication date: Apr-2023
https://doi.org/10.1109/ICDE55515.2023.00039
Show More Cited By

Index Terms

Parallel Peeling Algorithms
1. Theory of computation
  1. Design and analysis of algorithms
    1. Parallel algorithms
      1. Massively parallel algorithms
    2. Streaming, sublinear and near linear time algorithms
      1. Bloom filters and hashing
      2. Sketching and sampling
  2. Randomness, geometry and discrete structures
    1. Error-correcting codes

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Published In

cover image ACM Transactions on Parallel Computing

ACM Transactions on Parallel Computing Volume 3, Issue 1

Special Issue for SPAA 2014

June 2016

192 pages

ISSN:2329-4949

EISSN:2329-4957

DOI:10.1145/2965648

Editor:
Phillip B. Gibbons
Carnegie Mellon University, Pittsburgh, USA

Issue’s Table of Contents

Copyright © 2017 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 16 January 2017

Accepted: 01 March 2015

Revised: 01 March 2015

Received: 01 August 2014

Published in TOPC Volume 3, Issue 1

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Cited By

Arafat NKhan ARai AGhosh B(2023)Neighborhood-Based Hypergraph Core DecompositionProceedings of the VLDB Endowment10.14778/3598581.359858216:9(2061-2074)Online publication date: 1-May-2023
https://dl.acm.org/doi/10.14778/3598581.3598582
Choe MKim SYoo JShin KSingh ASun YAkoglu LGunopulos DYan XKumar ROzcan FYe J(2023)Classification of Edge-dependent Labels of Nodes in HypergraphsProceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3580305.3599274(298-309)Online publication date: 6-Aug-2023
https://dl.acm.org/doi/10.1145/3580305.3599274
Luo QYu DLiu YZheng YCheng XLin X(2023)Finer-Grained Engagement in Hypergraphs2023 IEEE 39th International Conference on Data Engineering (ICDE)10.1109/ICDE55515.2023.00039(423-435)Online publication date: Apr-2023
https://doi.org/10.1109/ICDE55515.2023.00039
Luo QYu DCai ZZheng YCheng XLin X(2023)Core maintenance for hypergraph streamsWorld Wide Web10.1007/s11280-023-01196-626:5(3709-3733)Online publication date: 25-Aug-2023
https://dl.acm.org/doi/10.1007/s11280-023-01196-6
Wang QZheng LHu AHuang YYao PGui CLiao XJin HXue JHardavellas NCampanoni SGrot BKarpuzcu U(2022)A Data-Centric Accelerator for High-Performance Hypergraph ProcessingProceedings of the 55th Annual IEEE/ACM International Symposium on Microarchitecture10.1109/MICRO56248.2022.00088(1326-1341)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1109/MICRO56248.2022.00088
Wang QZheng LYuan JHuang YYao PGui CHu ALiao XJin H(2022)Hardware-Accelerated Hypergraph Processing with Chain-Driven Scheduling2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA)10.1109/HPCA53966.2022.00022(184-198)Online publication date: Apr-2022
https://doi.org/10.1109/HPCA53966.2022.00022
Luo QYu DCai ZLin XWang GCheng X(2022)Toward maintenance of hypercores in large-scale dynamic hypergraphsThe VLDB Journal — The International Journal on Very Large Data Bases10.1007/s00778-022-00763-z32:3(647-664)Online publication date: 20-Sep-2022
https://dl.acm.org/doi/10.1007/s00778-022-00763-z
Hod RKrivelevich MMüller TNaor AWormald N(2022)Component Games on Random GraphsCombinatorica10.1007/s00493-022-5036-942:Suppl 1(1189-1229)Online publication date: 21-Sep-2022
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Gao PIsaev MMcKay B(2022)Sandwiching dense random regular graphs between binomial random graphsProbability Theory and Related Fields10.1007/s00440-022-01157-6184:1-2(115-158)Online publication date: 6-Aug-2022
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Luo QYu DCai ZLin XCheng X(2021)Hypercore Maintenance in Dynamic Hypergraphs2021 IEEE 37th International Conference on Data Engineering (ICDE)10.1109/ICDE51399.2021.00199(2051-2056)Online publication date: Apr-2021
https://doi.org/10.1109/ICDE51399.2021.00199
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