research-article

Linear-work greedy parallel approximate set cover and variants

Authors:

Guy E. Blelloch,

Kanat TangwongsanAuthors Info & Claims

SPAA '11: Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures

Pages 23 - 32

https://doi.org/10.1145/1989493.1989497

Published: 04 June 2011 Publication History

Abstract

We present parallel greedy approximation algorithms for set cover and related problems. These algorithms build on an algorithm for solving a graph problem we formulate and study called Maximal Nearly Independent Set (MaNIS)---a graph abstraction of a key component in existing work on parallel set cover.

We derive a randomized algorithm for MaNIS that has O(m) work and O(log² m) depth on input with m edges. Using MaNIS, we obtain RNC algorithms that yield a (1+ε)H_n-approximation for set cover, a (1 - 1/e -ε)-approximation for max cover and a (4 + ε)-approximation for min-sum set cover all in linear work; and an O(log* n)-approximation for asymmetric k-center for k ≤ log^O(1) n and a (1.861+ε)-approximation for metric facility location both in essentially the same work bounds as their sequential counterparts.

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https://doi.org/10.1109/TNSM.2023.3288738
Pham CPhu QHa D(2024)Fast Bicriteria Approximation Algorithm for Minimum Cost Submodular Cover ProblemComputational Data and Social Networks10.1007/978-981-97-0669-3_18(186-197)Online publication date: 29-Feb-2024
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Index Terms

Linear-work greedy parallel approximate set cover and variants
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

SPAA '11: Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures

June 2011

404 pages

ISBN:9781450307437

DOI:10.1145/1989493

Co-chairs:
Friedhelm Meyer auf der Heide
University of Paderborn, Germany
,
Rajmohan Rajaraman
Northeastern University, USA

Copyright © 2011 ACM.

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Published: 04 June 2011

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SPAA '11: 23rd ACM Symposium on Parallelism in Algorithms and Architectures

June 4 - 6, 2011

California, San Jose, USA

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Overall Acceptance Rate 447 of 1,461 submissions, 31%

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https://doi.org/10.1142/S0217595924500052
Wu JWu JChen LSun YWu Y(2024)Joint Dataset Reconstruction and Power Control for Distributed Training in D2D Edge NetworkIEEE Transactions on Network and Service Management10.1109/TNSM.2023.328873821:1(132-147)Online publication date: Feb-2024
https://doi.org/10.1109/TNSM.2023.3288738
Pham CPhu QHa D(2024)Fast Bicriteria Approximation Algorithm for Minimum Cost Submodular Cover ProblemComputational Data and Social Networks10.1007/978-981-97-0669-3_18(186-197)Online publication date: 29-Feb-2024
https://doi.org/10.1007/978-981-97-0669-3_18
DONG RIZUMI TKITAMURA NSUDO YMASUZAWA T(2023)Loosely-Stabilizing Algorithm on Almost Maximal Independent SetIEICE Transactions on Information and Systems10.1587/transinf.2023EDP7075E106.D:11(1762-1771)Online publication date: 1-Nov-2023
https://doi.org/10.1587/transinf.2023EDP7075
Pham CHa D(2023)A note for approximating the submodular cover problem over integer lattice with low adaptive and query complexitiesInformation Processing Letters10.1016/j.ipl.2023.106393182(106393)Online publication date: Aug-2023
https://doi.org/10.1016/j.ipl.2023.106393
Dhulipala LEisenstat DŁącki JMirrokni VShi JKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Hierarchical agglomerative graph clustering in poly-logarithmic depthProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3601936(22925-22940)Online publication date: 28-Nov-2022
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Hong WRan YZhang Z(2022)Parallel algorithms for minimum general partial dominating set and maximum budgeted dominating set in unit disk graphTheoretical Computer Science10.1016/j.tcs.2022.07.039932(13-20)Online publication date: Oct-2022
https://doi.org/10.1016/j.tcs.2022.07.039
Dhulipala LBlelloch GShun J(2021)Theoretically Efficient Parallel Graph Algorithms Can Be Fast and ScalableACM Transactions on Parallel Computing10.1145/34343938:1(1-70)Online publication date: 22-Apr-2021
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Jaleel HShamma J(2020)Distributed Submodular Minimization and Motion Planning Over Discrete State SpaceIEEE Transactions on Control of Network Systems10.1109/TCNS.2019.29339937:2(932-943)Online publication date: Jun-2020
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Chekuri CQuanrud KChan T(2019)Submodular function maximization in parallel via the multilinear relaxationProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310455(303-322)Online publication date: 6-Jan-2019
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