Constraint Satisfaction Problems: Complexity and Algorithms

TL;DR: An important class of problems in logics and database theory is given by fixing a first-order property ψ over a relational structure, and considering the model-checking problem for ψ, and a dichotomy is given for the class of ∃k∀-quantified graph properties.

TL;DR: The history of the Dichotomy Conjecture for the Constraint Satisfaction problem is surveyed, some of the approaches to this conjecture are outlined, and an algorithm is described that yields an answer to the conjecture.

TL;DR: It is shown that the reduced Gröbner basis of ideals whose varieties are closed under the majority polymorphism can be computed in polynomial time, which proves polynometric time solvability of the IMPd for these constrained problems.

TL;DR: It is proved that the IMP$_d$ for Boolean combinatorial ideals whose constraints are closed under the minority polymorphism can be solved in polynomial time.

TL;DR: The primary aim is to provide an accessible, unified framework, within which to present the algorithms including a new path consistency algorithm, to discuss their relationships and the may applications, both realized and potential of network consistency algorithms.

TL;DR: An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.

TL;DR: It is shown that while answering conjunctive queries is NP complete (general queries are PSPACE complete), one can find an implementation that is within a constant of optimal.

TL;DR: This paper isolates a class (of problems specified by) "monotone monadic SNP without inequality" which may exhibit a dichotomy, and explains the placing of all these restrictions by showing, essentially using Ladner's theorem, that classes obtained by using only two of the above three restrictions do not show this dichotomy.