Closure properties of constraints

@article{Jeavons1997ClosurePO,
  title={Closure properties of constraints},
  author={Peter Jeavons and David A. Cohen and Marc Gyssens},
  journal={J. ACM},
  year={1997},
  volume={44},
  pages={527-548}
}
Many combinatorial search problems can be expressed as “constraint satisfaction problems” and this class of problems is known to be NP-complete in general. In this paper, we investigate the subclasses that arise from restricting the possible constraint types. We first show that any set of constraints that does not give rise to an NP-complete class of problems must satisfy a certain type of algebraic closure condition. We then investigate all the different possible forms of this algebraic… Expand
An Algorithm for Constraint Satisfaction Problem
  • Dmitriy Zhuk
  • Mathematics, Computer Science
  • 2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)
  • 2017
TLDR
An algorithm is presented that solves Constraint Satisfaction Problem in polynomial time for constraint languages having a weak near unanimity polymorphism, which proves the remaining part of the conjecture. Expand
Constraint Satisfaction Problems and Finite Algebras
TLDR
It is shown that any restricted set of constraint types can be associated with a finite universal algebra and the result is a dichotomy theorem which significantly generalises Schaefer's dichotomy for the Generalised Satisfiability problem. Expand
Complexity of conservative constraint satisfaction problems
TLDR
This work completely characterize conservative constraint languages that give rise to polynomial time solvable CSP classes, and obtains a complete description of those (directed) graphs H for which the List H-Coloring problem is solvable in polynometric time. Expand
A Proof of CSP Dichotomy Conjecture
  • Dmitriy Zhuk
  • Computer Science, Mathematics
  • 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2017
TLDR
An algorithm is presented that solves Constraint Satisfaction Problem in polynomial time for constraint languages having a weak near unanimity polymorphism, which proves the remaining part of the conjecture. Expand
A Proof of the CSP Dichotomy Conjecture
TLDR
This article presents an algorithm that solves Constraint Satisfaction Problem in polynomial time for constraint languages having a weak near unanimity polymorphism, which proves the remaining part of the conjecture. Expand
Tractable conservative constraint satisfaction problems
  • A. Bulatov
  • Mathematics, Computer Science
  • 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.
  • 2003
TLDR
This work completely characterize conservative constraint languages that give rise to CSP classes solvable in polynomial time, and obtains a complete description of those (directed) graphs H for which the List H-Coloring problem is poynomial time solvable. Expand
Classifying the Complexity of Constraints Using Finite Algebras
TLDR
It is shown that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra is explored. Expand
New tractable constraint classes from old
Many applications in AI involve searching over a very large possibility space. Constraint satisfaction is a general problem-solving paradigm that expresses some of these search problems in a naturalExpand
Constraints and universal algebra
TLDR
It is shown that a constraint satisfaction problem instance can be viewed as a pair of relational structures, and the solutions to the problem are then the structure preserving mappings between these two relational structures. Expand
A dichotomy theorem for constraints on a three-element set
  • A. Bulatov
  • Mathematics, Computer Science
  • The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
  • 2002
TLDR
Every subclass of the CSP defined by a set of allowed constraints is either tractable or NP-complete, and the criterion separating them is that conjectured by Bulatov et al. (2001). Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 46 REFERENCES
A test for Tractability
TLDR
It is shown that any set of constraints must satisfy a certain type of algebraic closure condition in order to avoid NP-completeness. Expand
An Algebraic Characterization of Tractable Constraints
TLDR
A simple algebraic closure condition is described, and it is shown that this is both necessary and sufficient to ensure tractability in Boolean valued problems. Expand
A Unifying Framework for Tractable Constraints
TLDR
All known classes with this property may be characterized by a simple algebraic closure condition, and this condition provides a uniform test to establish whether a given set of constraints falls into any of the known tractable classes, and may therefore be solved efficiently. Expand
Characterising Tractable Constraints
TLDR
A set of constraints is identified which gives rise to a class of tractable problems and given polynomial time algorithms for solving such problems, and it is proved that the class of problems generated by any set of constraint not contained in this restricted set is NP-complete. Expand
Tractable Constraints on Ordered Domains
TLDR
A restricted set of contraints is identified which gives rise to a class of tractable problems which generalizes the notion of a Horn formula in propositional logic to larger domain sizes, and it is proved that the class of problems generated by any larger set of constraints is NP-complete. Expand
The complexity of satisfiability problems
TLDR
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. Expand
Derivation of Constraints and Database Relations
TLDR
It is shown that, given a set of relations R, it is possible to derive any other relation which is invariant under P, using only the projection, Cartesian product, and selection operators, together with the effectivedomain of R, provided that the effective domain contains at least three elements. Expand
Fast Parallel Constraint Satisfaction
  • L. Kirousis
  • Mathematics, Computer Science
  • Artif. Intell.
  • 1993
TLDR
It is shown here that a CSP with this type of constraint relations (and no restrictions on its graph) can be solved by an efficient (i.e., with polynomial time complexity) sequential algorithm. Expand
Monotone monadic SNP and constraint satisfaction
TLDR
The question whether every problem in CSP is either in P or is NP-complete is posed, and the class of constraint-satisfaction problems with respect to fixed templates is defined. Expand
Network-Based Heuristics for Constraint-Satisfaction Problems
TLDR
This paper identifies classes of problems that lend themselves to easy solutions, and develops algorithms that solve these problems optimally by generating heuristic advice based on both the sparseness found in the constraint network and the simplicity of tree-structured CSPs. Expand
...
1
2
3
4
5
...