The Structure of Tractable Constraint Satisfaction Problems

We give a survey of recent results on the complexity of constraint satisfaction problems. Our main emphasis is on tractable structural restrictions.

[1]  Jaroslav Nesetril,et al.  On the complexity of H-coloring , 1990, J. Comb. Theory, Ser. B.

[2]  Andrei A. Bulatov,et al.  Tractable conservative constraint satisfaction problems , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[3]  Peter Jeavons,et al.  Classifying the Complexity of Constraints Using Finite Algebras , 2005, SIAM J. Comput..

[4]  Dániel Marx,et al.  Constraint solving via fractional edge covers , 2006, SODA '06.

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

[6]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

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

[8]  Peter Jeavons,et al.  On the Algebraic Structure of Combinatorial Problems , 1998, Theor. Comput. Sci..

[9]  Derek G. Corneil,et al.  Complexity of finding embeddings in a k -tree , 1987 .

[10]  Jaroslav Nesetril,et al.  Complexity of Tree Homomorphisms , 1996, Discret. Appl. Math..

[11]  Georg Gottlob,et al.  Hypertree decompositions and tractable queries , 1998, J. Comput. Syst. Sci..

[12]  Thomas J. Schaefer,et al.  The complexity of satisfiability problems , 1978, STOC.

[13]  Phokion G. Kolaitis,et al.  Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics , 2002, CP.

[14]  Marc Gyssens,et al.  Closure properties of constraints , 1997, JACM.

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

[16]  Martin Grohe.  The complexity of homomorphism and constraint satisfaction problems seen from the other side , 2007, JACM.

[17]  Georg Gottlob,et al.  Hypertree width and related hypergraph invariants , 2007, Eur. J. Comb..

[18]  Hans L. Bodlaender.  A linear time algorithm for finding tree-decompositions of small treewidth , 1993, STOC '93.

[19]  Peter Jeavons,et al.  The complexity of maximal constraint languages , 2001, STOC '01.

[20]  Víctor Dalmau,et al.  Generalized majority-minority operations are tractable , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[21]  Xuding Zhu,et al.  Duality and Polynomial Testing of Tree Homomorphisms , 1996 .

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

[23]  Andrei A. Bulatov,et al.  A dichotomy theorem for constraint satisfaction problems on a 3-element set , 2006, JACM.

[24]  Tomás Feder,et al.  The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory , 1999, SIAM J. Comput..

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

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

[27]  Eugene C. Freuder.  Complexity of K-Tree Structured Constraint Satisfaction Problems , 1990, AAAI.

[28]  Andrei A. Bulatov.  H-Coloring dichotomy revisited , 2005, Theor. Comput. Sci..

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

[30]  Richard E. Ladner,et al.  On the Structure of Polynomial Time Reducibility , 1975, JACM.