Improved Algorithms for Sparse MAX-SAT and MAX-k-CSP

Ruiwen Chen; Rahul Santhanam

doi:10.1007/978-3-319-24318-4_4

Improved Algorithms for Sparse MAX-SAT and MAX-k-CSP

Ruiwen Chen, Rahul Santhanam

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We give improved deterministic algorithms solving sparse instances of MAX-SAT and MAX-k-CSP. For instances with n variables and cn clauses (constraints), we give algorithms running in time poly(n)⋅2^n(1−μ) for
μ=Ω(1/c) and polynomial space solving MAX-SAT and MAX-k-SAT,
μ=Ω(1√c) and exponential space solving MAX-SAT and MAX-k-SAT,
μ=Ω(1/ck²) and polynomial space solving MAX-k-CSP,
μ=Ω(1/√ck³) and exponential space solving MAX-k-CSP.
The previous MAX-SAT algorithms have savings μ=Ω(1/c²log²c) for running in polynomial space [15] and μ=Ω(1/clogc) for exponential space [5]. We also give an algorithm with improved savings for satisfiability of depth-2 threshold circuits with cn wires.

Original language	English
Title of host publication	Theory and Applications of Satisfiability Testing -- SAT 2015
Editors	Marijn Heule, Sean Weaver
Place of Publication	Cham
Publisher	Springer International Publishing
Pages	33-45
Number of pages	13
ISBN (Electronic)	978-3-319-24318-4
ISBN (Print)	978-3-319-24317-7
DOIs	https://doi.org/10.1007/978-3-319-24318-4_4
Publication status	Published - 27 Oct 2015
Event	18th International Conference on Theory and Applications of Satisfiability Testing - Austin, United States Duration: 24 Sep 2015 → 27 Sep 2015

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer, Cham
Volume	9340
ISSN (Print)	1611-3349
ISSN (Electronic)	0302-9743

Conference

Conference	18th International Conference on Theory and Applications of Satisfiability Testing
Abbreviated title	SAT 2015
Country	United States
City	Austin
Period	24/09/15 → 27/09/15

Access to Document

10.1007/978-3-319-24318-4_4

TR15-112Accepted author manuscript, 639 KB

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ALUnif - Algorithms and Lower Bounds: A Unified Approach
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Cite this

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title = "Improved Algorithms for Sparse MAX-SAT and MAX-k-CSP",

abstract = "We give improved deterministic algorithms solving sparse instances of MAX-SAT and MAX-k-CSP. For instances with n variables and cn clauses (constraints), we give algorithms running in time poly(n)⋅2n(1−μ) forμ=Ω(1/c) and polynomial space solving MAX-SAT and MAX-k-SAT,μ=Ω(1√c) and exponential space solving MAX-SAT and MAX-k-SAT,μ=Ω(1/ck2) and polynomial space solving MAX-k-CSP,μ=Ω(1/√ck3) and exponential space solving MAX-k-CSP.The previous MAX-SAT algorithms have savings μ=Ω(1/c2log2c) for running in polynomial space [15] and μ=Ω(1/clogc) for exponential space [5]. We also give an algorithm with improved savings for satisfiability of depth-2 threshold circuits with cn wires.",

author = "Ruiwen Chen and Rahul Santhanam",

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doi = "10.1007/978-3-319-24318-4_4",

language = "English",

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series = "Lecture Notes in Computer Science ",

publisher = "Springer International Publishing",

pages = "33--45",

editor = "Marijn Heule and Sean Weaver",

booktitle = "Theory and Applications of Satisfiability Testing -- SAT 2015",

note = "18th International Conference on Theory and Applications of Satisfiability Testing, SAT 2015 ; Conference date: 24-09-2015 Through 27-09-2015",

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Chen, R & Santhanam, R 2015, Improved Algorithms for Sparse MAX-SAT and MAX-k-CSP. in M Heule & S Weaver (eds), Theory and Applications of Satisfiability Testing -- SAT 2015. Lecture Notes in Computer Science , vol. 9340, Springer International Publishing, Cham, pp. 33-45, 18th International Conference on Theory and Applications of Satisfiability Testing, Austin, United States, 24/09/15. https://doi.org/10.1007/978-3-319-24318-4_4

Improved Algorithms for Sparse MAX-SAT and MAX-k-CSP. / Chen, Ruiwen; Santhanam, Rahul.

Theory and Applications of Satisfiability Testing -- SAT 2015. ed. / Marijn Heule; Sean Weaver. Cham : Springer International Publishing, 2015. p. 33-45 (Lecture Notes in Computer Science ; Vol. 9340).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - We give improved deterministic algorithms solving sparse instances of MAX-SAT and MAX-k-CSP. For instances with n variables and cn clauses (constraints), we give algorithms running in time poly(n)⋅2n(1−μ) forμ=Ω(1/c) and polynomial space solving MAX-SAT and MAX-k-SAT,μ=Ω(1√c) and exponential space solving MAX-SAT and MAX-k-SAT,μ=Ω(1/ck2) and polynomial space solving MAX-k-CSP,μ=Ω(1/√ck3) and exponential space solving MAX-k-CSP.The previous MAX-SAT algorithms have savings μ=Ω(1/c2log2c) for running in polynomial space [15] and μ=Ω(1/clogc) for exponential space [5]. We also give an algorithm with improved savings for satisfiability of depth-2 threshold circuits with cn wires.

AB - We give improved deterministic algorithms solving sparse instances of MAX-SAT and MAX-k-CSP. For instances with n variables and cn clauses (constraints), we give algorithms running in time poly(n)⋅2n(1−μ) forμ=Ω(1/c) and polynomial space solving MAX-SAT and MAX-k-SAT,μ=Ω(1√c) and exponential space solving MAX-SAT and MAX-k-SAT,μ=Ω(1/ck2) and polynomial space solving MAX-k-CSP,μ=Ω(1/√ck3) and exponential space solving MAX-k-CSP.The previous MAX-SAT algorithms have savings μ=Ω(1/c2log2c) for running in polynomial space [15] and μ=Ω(1/clogc) for exponential space [5]. We also give an algorithm with improved savings for satisfiability of depth-2 threshold circuits with cn wires.

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M3 - Conference contribution

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ER -

Improved Algorithms for Sparse MAX-SAT and MAX-k-CSP

Abstract

Publication series

Conference

Access to Document

ALUnif - Algorithms and Lower Bounds: A Unified Approach

Cite this