The Order Encoding: From Tractable CSP to Tractable SAT

Many mathematical and practical problems can be expressed as constraint satisfaction problems (CSPs). The general CSP is known to be NP-complete, but many different conditions have been identified which are sufficient to ensure that classes of instances satisfying those conditions are tractable, that is, solvable in polynomial time [1,2,3,4,7].

[1]  Mutsunori Banbara,et al.  Compiling finite linear CSP into SAT , 2006, Constraints.

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

[3]  Hubie Chen,et al.  Arc consistency and friends , 2011, J. Log. Comput..

[4]  Marc Gyssens,et al.  A unified theory of structural tractability for constraint satisfaction problems , 2008, J. Comput. Syst. Sci..

[5]  Pascal Van Hentenryck,et al.  Constraint Satisfaction over Connected Row Convex Constraints , 1997, Artif. Intell..

[6]  Carlos Ansótegui,et al.  Mapping Problems with Finite-Domain Variables into Problems with Boolean Variables , 2004, SAT.

[7]  Justyna Petke,et al.  Local Consistency and SAT-Solvers , 2010, CP.

[8]  Christian Bessiere,et al.  Theoretical analysis of singleton arc consistency and its extensions , 2008, Artif. Intell..

[9]  Martin C. Cooper,et al.  Characterising Tractable Constraints , 1994, Artif. Intell..

[10]  Peter Jeavons,et al.  Building tractable disjunctive constraints , 2000, J. ACM.

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

[12]  David Cohen,et al.  Principles and Practice of Constraint Programming - CP 2010 - 16th International Conference, CP 2010, St. Andrews, Scotland, UK, September 6-10, 2010. Proceedings , 2010, CP.

[13]  Steven David Prestwich,et al.  CNF Encodings , 2021, Handbook of Satisfiability.

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

[15]  Johannes Klaus Fichte,et al.  Clause-Learning Algorithms with Many Restarts and Bounded-Width Resolution , 2011, J. Artif. Intell. Res..

[16]  Martin C. Cooper,et al.  Tractable Constraints on Ordered Domains , 1995, Artif. Intell..

[17]  James M. Crawford,et al.  Experimental Results on the Application of Satisfiability Algorithms to Scheduling Problems , 1994, AAAI.

[18]  Jean H. Gallier,et al.  Linear-Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae , 1984, J. Log. Program..

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

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

[21]  Sharad Malik,et al.  The Quest for Efficient Boolean Satisfiability Solvers , 2002, CAV.

[22]  Holger H. Hoos SAT-Encodings, Search Space Structure, and Local Search Performance , 1999, IJCAI.

[23]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.