Guarantees and limits of preprocessing in constraint satisfaction and reasoning

• Published in: Artificial intelligence Vol. 216; pp. 1 - 19
• Main Authors: Gaspers, Serge, Szeider, Stefan
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier B.V 01.11.2014; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Artificial intelligence; Combinatorial analysis; Computational complexity; Computer science; control theory; systems; Constraint satisfaction; Constrictions; Exact sciences and technology; Fixed-parameter tractability; Kernelization; Kernels; Learning and adaptive systems; Polynomials; Preprocessing; Reasoning; Tasks; Theoretical computing; Constraint satisfaction; Reasoning; Fixed-parameter tractability; Computational complexity; Kernelization; Bayes estimation; Energy analysis; Combinatorial problem; Worst case method; Combinatorial optimization; Circumscription; Polynomial time; Polynomial function; Kernel function; Reduction; Satisfiability
• ISSN: 0004-3702; 1872-7921
• DOI: 10.1016/j.artint.2014.06.006

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability, Nonmonotonic and Bayesian Reasoning under structural restrictions. All these problems involve two tasks: (i) identifying the structure in the input as required by the restriction, and (ii) using the identified structure to solve the reasoning task efficiently. We show that for most of the considered problems, task (i) admits a polynomial-time preprocessing to a problem kernel whose size is polynomial in a structural problem parameter of the input, in contrast to task (ii) which does not admit such a reduction to a problem kernel of polynomial size, subject to a complexity theoretic assumption. As a notable exception we show that the consistency problem for the AtMost-NValue constraint admits a polynomial kernel consisting of a quadratic number of variables and domain values. Our results provide a firm worst-case guarantees and theoretical boundaries for the performance of polynomial-time preprocessing algorithms for the considered problems.