research-article

Faster k-SAT algorithms using biased-PPSZ

Authors:

Thomas Dueholm Hansen,

Uri ZwickAuthors Info & Claims

STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

June 2019

Pages 578 - 589

https://doi.org/10.1145/3313276.3316359

Published: 23 June 2019 Publication History

Abstract

The PPSZ algorithm, due to Paturi, Pudlak, Saks and Zane, is currently the fastest known algorithm for the k-SAT problem, for every k>3. For 3-SAT, a tiny improvement over PPSZ was obtained by Hertli. We introduce a biased version of the PPSZ algorithm using which we obtain an improvement over PPSZ for every k≥ 3. For k=3 we also improve on Herli’s result and get a much more noticeable improvement over PPSZ, though still relatively small. In particular, for Unique 3-SAT, we improve the current bound from 1.308ⁿ to 1.307ⁿ.

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Index Terms

Faster k-SAT algorithms using biased-PPSZ
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

June 2019

1258 pages

ISBN:9781450367059

DOI:10.1145/3313276

General Chair:
Moses Charikar
Stanford University
,
Program Chair:
Edith Cohen
Google, USA / Tel Aviv University, Israel

Copyright © 2019 ACM.

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 23 June 2019

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Funding Sources

Israel Science Foundation
German-Israeli Foundation for Scientific Research and Development
Villum Fonden
Blavatnik Family Foundation

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STOC '19

Sponsor:

SIGACT

STOC '19: 51st Annual ACM SIGACT Symposium on the Theory of Computing

June 23 - 26, 2019

AZ, Phoenix, USA

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Yang SZi WWu BGuo CZhang JSun X(2024)Efficient Quantum Circuit Synthesis for SAT-Oracle With Limited Ancillary QubitIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2023.332597443:3(868-877)Online publication date: Mar-2024
https://doi.org/10.1109/TCAD.2023.3325974
Rennela MBrand SLaarman ADunjko V(2023)Hybrid divide-and-conquer approach for tree search algorithmsQuantum10.22331/q-2023-03-23-9597(959)Online publication date: 23-Mar-2023
https://doi.org/10.22331/q-2023-03-23-959
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Scheder D(2022)PPSZ is better than you think2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00028(205-216)Online publication date: Feb-2022
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Lagerkvist VWahlström M(2021)The (Coarse) Fine-Grained Structure of NP-Hard SAT and CSP ProblemsACM Transactions on Computation Theory10.1145/349233614:1(1-54)Online publication date: 15-Dec-2021
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