NDLI: Classifying the Complexity of Constraints Using Finite Algebras

Please wait, while we are loading the content...

Classifying the Complexity of Constraints Using Finite Algebras

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Krokhin, Andrei Jeavons, Peter Bulatov, Andrei
Copyright Year	2005
Abstract	Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. Here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra. Hence, we completely translate the problem of classifying the complexity of restricted constraint satisfaction problems into the language of universal algebra.We introduce a notion of "tractable algebra," and investigate how the tractability of an algebra relates to the tractability of the smaller algebras which may be derived from it, including its subalgebras and homomorphic images. This allows us to reduce significantly the types of algebras which need to be classified. Using our results we also show that if the decision problem associated with a given collection of constraint types can be solved efficiently, then so can the corresponding search problem. We then classify all finite strictly simple surjective algebras with respect to tractability, obtaining a dichotomy theorem which generalizes Schaefer's dichotomy for the generalized satisfiability problem. Finally, we suggest a possible general algebraic criterion for distinguishing the tractable and intractable cases of the constraint satisfaction problem.
Starting Page	720
Ending Page	742
Page Count	23
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539700376676
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	3
Volume Number	34
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-27
Access Restriction	Subscribed
Subject Keyword	Analysis of algorithms and problem complexity Applications of universal algebra in computer science dichotomy theorem constraint satisfaction problem universal algebra
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Classifying the complexity of constraints using finite algebras (2005)

The Complexity of Quantified Constraint Satisfaction: Collapsibility, Sink Algebras, and the Three-Element Case

A Simple Algorithm for Mal'tsev Constraints

An Effective Dichotomy for the Counting Constraint Satisfaction Problem

A Dichotomy Theorem for the Resolution Complexity of Random Constraint Satisfaction Problems

Tractability and Learnability Arising from Algebras with Few Subpowers

Nonnegative Weighted #CSP: An Effective Complexity Dichotomy

The Dichotomy for Conservative Constraint Satisfaction Problems Revisited

Constraint Satisfaction Problems on Intervals and Lengths

Classifying the Complexity of Constraints Using Finite Algebras

Similar Documents

Classifying the complexity of constraints using finite algebras (2005)

The Complexity of Quantified Constraint Satisfaction: Collapsibility, Sink Algebras, and the Three-Element Case

A Simple Algorithm for Mal'tsev Constraints

An Effective Dichotomy for the Counting Constraint Satisfaction Problem

A Dichotomy Theorem for the Resolution Complexity of Random Constraint Satisfaction Problems

Tractability and Learnability Arising from Algebras with Few Subpowers

Nonnegative Weighted #CSP: An Effective Complexity Dichotomy

The Dichotomy for Conservative Constraint Satisfaction Problems Revisited

Constraint Satisfaction Problems on Intervals and Lengths

Classifying the Complexity of Constraints Using Finite Algebras