Fixed-parameter complexity in AI and nonmonotonic reasoning

Many relevant intractable problems become tractable if some problem parameter is fixed. However, various problems exhibit very different computational properties, depending on how the runtime required for solving them is related to the fixed parameter chosen. The theory of parameterized complexity d...

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Published in:	Artificial intelligence Vol. 138; no. 1; pp. 55 - 86
Main Authors:	Gottlob, Georg, Scarcello, Francesco, Sideri, Martha
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.06.2002
Subjects:	Artificial intelligence Circumscription Conjunctive queries Constraint satisfaction Fixed-parameter tractability Knowledge representation Logic programming Nonmonotonic reasoning Parameterized complexity Prime implicants Stable models Logic programming Nonmonotonic reasoning Constraint satisfaction Stable models Prime implicants Fixed-parameter tractability Parameterized complexity Conjunctive queries Circumscription
ISSN:	0004-3702, 1872-7921
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Abstract	Many relevant intractable problems become tractable if some problem parameter is fixed. However, various problems exhibit very different computational properties, depending on how the runtime required for solving them is related to the fixed parameter chosen. The theory of parameterized complexity deals with such issues, and provides general techniques for identifying fixed-parameter tractable and fixed-parameter intractable problems. We study the parameterized complexity of various problems in AI and nonmonotonic reasoning. We show that a number of relevant parameterized problems in these areas are fixed-parameter tractable. Among these problems are constraint satisfaction problems with bounded treewidth and fixed domain, restricted forms of conjunctive database queries, restricted satisfiability problems, propositional logic programming under the stable model semantics where the parameter is the dimension of a feedback vertex set of the program's dependency graph, and circumscriptive inference from a positive k-CNF restricted to models of bounded size. We also show that circumscriptive inference from a general propositional theory, when the attention is restricted to models of bounded size, is fixed-parameter intractable and is actually complete for a novel fixed-parameter complexity class.
AbstractList	Article included in a special issue devoted to the theme: Knowledge presentation and logic programming. Many relevant intractable problems become tractable if some problem parameter is fixed. However, various problems exhibit very different computational properties, depending on how the runtime required for solving them is related to the fixed parameter chosen. The theory of parameterized complexity deals with such issues, and provides general techniques for identifying fixed-parameter tractable and fixed-parameter intractable problems. Describes a study of the parameterized complexity of various problems in artificial intelligence and non monotonic reasoning. Shows that a number of relevant parameterized problems in these areas are fixed parameter tractable. Among these problems are constraint satisfaction problems with bounded treewidth and fixed domain, restricted forms of conjunctive database queries, restricted satisfiability problems, propositional logic programming under the stable model semantics where the parameter is the dimension of a feedback vertex set of the program's dependency graph, and circumscriptive inference from a positive k-CNF restricted to models of bounded size. (Original abstract - amended) Many relevant intractable problems become tractable if some problem parameter is fixed. However, various problems exhibit very different computational properties, depending on how the runtime required for solving them is related to the fixed parameter chosen. The theory of parameterized complexity deals with such issues, and provides general techniques for identifying fixed-parameter tractable and fixed-parameter intractable problems. We study the parameterized complexity of various problems in AI and nonmonotonic reasoning. We show that a number of relevant parameterized problems in these areas are fixed-parameter tractable. Among these problems are constraint satisfaction problems with bounded treewidth and fixed domain, restricted forms of conjunctive database queries, restricted satisfiability problems, propositional logic programming under the stable model semantics where the parameter is the dimension of a feedback vertex set of the program's dependency graph, and circumscriptive inference from a positive k-CNF restricted to models of bounded size. We also show that circumscriptive inference from a general propositional theory, when the attention is restricted to models of bounded size, is fixed-parameter intractable and is actually complete for a novel fixed-parameter complexity class.
Author	Gottlob, Georg Scarcello, Francesco Sideri, Martha
Author_xml	– sequence: 1 givenname: Georg surname: Gottlob fullname: Gottlob, Georg email: gottlob@dbai.tuwien.ac.at organization: Institut für Informationssysteme, Technische Universität Wien, A-1040 Vienna, Austria – sequence: 2 givenname: Francesco surname: Scarcello fullname: Scarcello, Francesco email: scarcello@deis.unical.it organization: Dipartimento di Elettronica, Informatica e Sistemistica, Università della Calabria, I-87036 Rende (CS), Italy – sequence: 3 givenname: Martha surname: Sideri fullname: Sideri, Martha email: sideri@aueb.gr organization: Department of Informatics, Athens University of Economics and Business, GR-10434 Athens, Greece
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Keywords	Logic programming Nonmonotonic reasoning Constraint satisfaction Stable models Prime implicants Fixed-parameter tractability Parameterized complexity Conjunctive queries Circumscription
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Snippet	Many relevant intractable problems become tractable if some problem parameter is fixed. However, various problems exhibit very different computational... Article included in a special issue devoted to the theme: Knowledge presentation and logic programming. Many relevant intractable problems become tractable if...
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SubjectTerms	Artificial intelligence Circumscription Conjunctive queries Constraint satisfaction Fixed-parameter tractability Knowledge representation Logic programming Nonmonotonic reasoning Parameterized complexity Prime implicants Stable models
Title	Fixed-parameter complexity in AI and nonmonotonic reasoning
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