Counting solutions to CSP using generating polynomials

Daniel Berend; Shahar Golan

doi:10.1016/j.jda.2014.01.004

Counting solutions to CSP using generating polynomials

Daniel Berend
, Shahar Golan

Research output: Contribution to journal › Article › peer-review

Abstract

Constraint Satisfaction Problems (CSPs) are ubiquitous in computer science and specifically in AI. This paper presents a method of solving the counting problem for a wide class of CSPs using generating polynomials. Analysis of our method shows that it is much more efficient than the classic dynamic programming approach. For example, in the case of #SAT, our algorithm improves a result of Samer and Szeider. The presented algorithms mostly use algebraic operations on multivariate polynomials, which allows application of known optimizations and makes it possible to use existing software to implement them easily.

Original language	English
Pages (from-to)	89-97
Number of pages	9
Journal	Journal of Discrete Algorithms
Volume	26
DOIs	https://doi.org/10.1016/j.jda.2014.01.004
State	Published - 1 Jan 2014

Keywords

CNF SAT
Constraint satisfaction problem
Counting problem
Generating functions
Treewidth

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jda.2014.01.004

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abstract = "Constraint Satisfaction Problems (CSPs) are ubiquitous in computer science and specifically in AI. This paper presents a method of solving the counting problem for a wide class of CSPs using generating polynomials. Analysis of our method shows that it is much more efficient than the classic dynamic programming approach. For example, in the case of \#SAT, our algorithm improves a result of Samer and Szeider. The presented algorithms mostly use algebraic operations on multivariate polynomials, which allows application of known optimizations and makes it possible to use existing software to implement them easily.",

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journal = "Journal of Discrete Algorithms",

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AU - Golan, Shahar

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AB - Constraint Satisfaction Problems (CSPs) are ubiquitous in computer science and specifically in AI. This paper presents a method of solving the counting problem for a wide class of CSPs using generating polynomials. Analysis of our method shows that it is much more efficient than the classic dynamic programming approach. For example, in the case of #SAT, our algorithm improves a result of Samer and Szeider. The presented algorithms mostly use algebraic operations on multivariate polynomials, which allows application of known optimizations and makes it possible to use existing software to implement them easily.

KW - CNF SAT

KW - Constraint satisfaction problem

KW - Counting problem

KW - Generating functions

KW - Treewidth

UR - https://www.scopus.com/pages/publications/84899628726

U2 - 10.1016/j.jda.2014.01.004

DO - 10.1016/j.jda.2014.01.004

M3 - Article

AN - SCOPUS:84899628726

SN - 1570-8667

VL - 26

SP - 89

EP - 97

JO - Journal of Discrete Algorithms

JF - Journal of Discrete Algorithms

ER -

Counting solutions to CSP using generating polynomials

Abstract

Keywords

ASJC Scopus subject areas

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