Constraint satisfaction with bounded treewidth revisited

We consider the constraint satisfaction problem (CSP) parameterized by the treewidth of primal, dual, and incidence graphs, combined with several other basic parameters such as domain size and arity. We determine all combinations of the considered parameters that admit fixed-parameter tractability.

[1]  Rina Dechter,et al.  Tractable Structures for Constraint Satisfaction Problems , 2006, Handbook of Constraint Programming.

[2]  Phokion G. Kolaitis,et al.  Conjunctive-query containment and constraint satisfaction , 1998, PODS.

[3]  Marc Gyssens,et al.  A Unified Theory of Structural Tractability for Constraint Satisfaction and Spread Cut Decomposition , 2005, IJCAI.

[4]  Mihalis Yannakakis,et al.  On the Complexity of Database Queries , 1999, J. Comput. Syst. Sci..

[5]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[6]  Hans L. Bodlaender,et al.  A Partial k-Arboretum of Graphs with Bounded Treewidth , 1998, Theor. Comput. Sci..

[7]  Peter Jeavons,et al.  The Complexity of Constraint Languages , 2006, Handbook of Constraint Programming.

[8]  Georg Gottlob,et al.  Fixed-parameter complexity in AI and nonmonotonic reasoning , 1999, Artif. Intell..

[9]  Bruce A. Reed,et al.  Finding approximate separators and computing tree width quickly , 1992, STOC '92.

[10]  Toby Walsh,et al.  Handbook of Constraint Programming , 2006, Handbook of Constraint Programming.

[11]  Mihalis Yannakakis,et al.  Algorithms for Acyclic Database Schemes , 1981, VLDB.

[12]  Hans L. Bodlaender,et al.  A linear time algorithm for finding tree-decompositions of small treewidth , 1993, STOC.

[13]  Georg Gottlob,et al.  Hypertree Decompositions: Structure, Algorithms, and Applications , 2005, WG.

[14]  Eugene C. Freuder.  A sufficient condition for backtrack-bounded search , 1985, JACM.

[15]  Ton Kloks,et al.  Efficient and Constructive Algorithms for the Pathwidth and Treewidth of Graphs , 1993, J. Algorithms.

[16]  Rolf Niedermeier,et al.  Invitation to Fixed-Parameter Algorithms , 2006 .

[17]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[18]  Marko Samer,et al.  Fixed-Parameter Tractability , 2021, Handbook of Satisfiability.

[19]  Jörg Flum,et al.  Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series) , 2006 .

[20]  Georg Gottlob,et al.  Hypertree Decompositions: A Survey , 2001, MFCS.

[21]  Rina Dechter,et al.  Tree Clustering for Constraint Networks , 1989, Artif. Intell..

[22]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .

[23]  Hubie Chen,et al.  Beyond Hypertree Width: Decomposition Methods Without Decompositions , 2005, CP.

[24]  Martin Grohe,et al.  Constraint solving via fractional edge covers , 2006, SODA 2006.

[25]  Russell Impagliazzo,et al.  Which Problems Have Strongly Exponential Complexity? , 2001, J. Comput. Syst. Sci..

[26]  Stefan Szeider,et al.  On Fixed-Parameter Tractable Parameterizations of SAT , 2003, SAT.

[27]  Marko Samer,et al.  Constraint satisfaction with bounded treewidth revisited , 2006, J. Comput. Syst. Sci..

[28]  Marko Samer,et al.  Algorithms for Propositional Model Counting , 2007, LPAR.

[29]  Jörg Flum,et al.  Parameterized Complexity Theory , 2006, Texts in Theoretical Computer Science. An EATCS Series.