Full Constraint Satisfaction Problems

  title={Full Constraint Satisfaction Problems},
  author={Tom{\'a}s Feder and Pavol Hell},
  journal={SIAM J. Comput.},
Feder and Vardi have conjectured that all constraint satisfaction problems to a fixed structure (constraint language) are polynomial or NP-complete. This so-called dichotomy conjecture remains open, although it has been proved in a number of special cases. Most recently, Bulatov has verified the conjecture for conservative structures, i.e., structures which contain all possible unary relations. We explore three different implications of Bulatov's result. First, the above dichotomy can be… 

Colouring, constraint satisfaction, and complexity

Constraint satisfaction: a personal perspective

  • T. Feder
  • Mathematics
    Electron. Colloquium Comput. Complex.
  • 2006
It can be shown, under the same assumption, that whether a problem in NP is polynomial time solvable or NP-complete is undecidable, from the undecidablity of the halting problem.

Colouring , Constraint Satisfaction , and Complexity For Aleš Pultr on the Occasion of his 70 th Birthday Pavol Hell

Constraint satisfaction problems have enjoyed much attention since the early seventies, and in the last decade have become also a focus of attention amongst theoreticians. Graph colourings are a

Bounded Tree-Width and CSP-Related Problems

It is proved, under a certain complexity-theoretic assumption, that this list homomorphism problem is solvable in polynomial time if and only if all structures in C have bounded tree-width.

Obstructions to Trigraph Homomorphisms

This thesis develops new tools and uses them to find all such graph partition problems with up to five parts, and observes that these problems are automatically polynomial time solvable.

Clique versus independent set

Advances on the List Stubborn Problem

This work polynomially reduces the general list stubborn instance to a particular instance with a structured graph and only two types of lists, and shows that this particular list 4-partition problem is polynOMially equivalent to a nonlist problem, named twofold stubborn problem.

Tractability in constraint satisfaction problems: a survey

Although this work focuses on the classical CSP, it also covers its important extensions to infinite domains and optimisation, as well as #CSP and QCSP.

Obstructions to partitions of chordal graphs

The stubborn problem is stubborn no more: a polynomial algorithm for 3-compatible colouring and the stubborn list partition problem

A polynomial time algorithm is presented for the 3-Compatible colouring problem, where each edge is assigned one of 3 possible colours and it is proposed to assign one of those 3 colours to each vertex in such a way that no edge has the same colour as both of its endpoints.



A dichotomy theorem for constraints on a three-element set

  • A. Bulatov
  • Computer Science
    The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
  • 2002
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).

Dichotomies for classes of homomorphism problems involving unary functions

Tractable conservative constraint satisfaction problems

  • A. Bulatov
  • Computer Science
    18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.
  • 2003
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.

The complexity of satisfiability problems

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.

Closure properties of constraints

This paper investigates the subclasses that arise from restricting the possible constraint types, and shows 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.

Classifying the Complexity of Constraints Using Finite Algebras

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.

From Graph Colouring to Constraint Satisfaction: There and Back Again

Graph colourings may be viewed as special constraint satisfaction problems. The class of k-colouring problems enjoys a well known dichotomy of complexity — these problems are polynomial time solvable

Fanout limitations on constraint systems

  • T. Feder
  • Mathematics
    Theor. Comput. Sci.
  • 2001

Generalized Satisfability with Limited Occurrences per Variable: A Study through Delta-Matroid Parity

It is shown that 3 occurrences per variable suffice to make these problems as hard as their unrestricted version, and two new families of generalized satisfiability problems are identified, called local and binary, that are polynomially solvable when only 2 occurrences per variables are allowed.

Algorithmic aspects of type inference with subtypes

It is NP-hard to decide whether a lambda term has a type with respect to a fixed subtype hierarchy (involving only atomic type names), and PSPACE upper bounds for deciding polymorphic typability are given.