research-article

The Randomized Local Computation Complexity of the Lovász Local Lemma

Authors:

Sebastian Brandt,

Christoph Grunau,

Václav RozhoňAuthors Info & Claims

PODC'21: Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

Pages 307 - 317

https://doi.org/10.1145/3465084.3467931

Published: 23 July 2021 Publication History

Abstract

The Local Computation Algorithm (LCA) model is a popular model in the field of sublinear-time algorithms that measures the complexity of an algorithm by the number of probes the algorithm makes in the neighborhood of one node to determine that node's output. In this paper we show that the randomized LCA complexity of the Lovász Local Lemma (LLL) on constant degree graphs is Θ(log n). The lower bound follows by proving an Ω(log n) lower bound for the Sinkless Orientation problem introduced in [Brandt et al. STOC 2016]. This answers a question of [Rosenbaum, Suomela PODC 2020]. Additionally, we show that every randomized LCA algorithm for a locally checkable problem with a probe complexity of o(√log n ) can be turned into a deterministic LCA algorithm with a probe complexity of O(log^* n). This improves exponentially upon the currently best known speed-up result from o(log log n) to O(log^* n) implied by the result of [Chang, Pettie FOCS 2017] in the LOCAL model. Finally, we show that for every fixed constant c ≥ 2, the deterministic VOLUME complexity of c-coloring a bounded degree tree is Θ(n), where the VOLUME model is a close relative of the LCA model that was recently introduced by [Rosenbaum, Suomela PODC 2020].

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Cited By

Lange JVasilyan A(2023)Agnostic proper learning of monotone functions: beyond the black-box correction barrier2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00068(1149-1170)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00068
Lange JRubinfeld RVasilyan A(2022)Properly learning monotone functions via local correction2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00015(75-86)Online publication date: Oct-2022
https://doi.org/10.1109/FOCS54457.2022.00015

Index Terms

The Randomized Local Computation Complexity of the Lovász Local Lemma
1. Theory of computation
  1. Design and analysis of algorithms
    1. Streaming, sublinear and near linear time algorithms

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cover image ACM Conferences

PODC'21: Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

July 2021

590 pages

ISBN:9781450385480

DOI:10.1145/3465084

General Chair:
Avery Miller
University of Manitoba, Canada
,
Program Chair:
Keren Censor-Hillel
Technion, Israel

Copyright © 2021 ACM.

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Publication History

Published: 23 July 2021

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Horizon 2020 research and innovation programme

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PODC '21

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PODC '21: ACM Symposium on Principles of Distributed Computing

July 26 - 30, 2021

Virtual Event, Italy

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Overall Acceptance Rate 740 of 2,477 submissions, 30%

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Cited By

Lange JVasilyan A(2023)Agnostic proper learning of monotone functions: beyond the black-box correction barrier2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00068(1149-1170)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00068
Lange JRubinfeld RVasilyan A(2022)Properly learning monotone functions via local correction2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00015(75-86)Online publication date: Oct-2022
https://doi.org/10.1109/FOCS54457.2022.00015

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