• Corpus ID: 28271359

The Constraint Satisfaction Problem: Complexity and Approximability

@inproceedings{Fraser2017TheCS,
  title={The Constraint Satisfaction Problem: Complexity and Approximability},
  author={A. S. Fraser and Andrei A. Krokhin},
  booktitle={The Constraint Satisfaction Problem},
  year={2017}
}
Constraint satisfaction has always played a central role in computational complexity theory; appropriate versions of CSPs are classical complete problems for most standard complexity classes. CSPs constitute a very rich and yet sufficiently manageable class of problems to give a good perspective on general computational phenomena. For instance, they help to understand which mathematical properties make a computational problem tractable (in a wide sense, e.g., polynomial-time solvable, non… 
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32 Citations

Algebraic approach to promise constraint satisfaction
TLDR
A new class of problems that can be viewed as algebraic versions of the (Gap) Label Cover problem are introduced, and it is shown that every PCSP with a fixed constraint language is equivalent to a problem of this form.
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.
Fine-Grained Time Complexity of Constraint Satisfaction Problems
TLDR
Under the exponential-time hypothesis (ETH), the existence of subexponential algorithms for finite-domain NP-complete CSPΓ problems is ruled out and a relation SD is identified such that the time complexity of the NP- complete CSP({SD}) is a lower bound for all NP- Complete CSPs of this kind.
Algebraic Theory of Promise Constraint Satisfaction Problems, First Steps
  • L. Barto
  • Mathematics, Computer Science
    FCT
  • 2019
TLDR
This paper explains an extension of this theory to a much broader class of computational problems, the promise CSPs, which includes relaxed versions of C SPs such as the problem of finding a 137-coloring of a 3-colorable graph.
The Complexity of the Distributed Constraint Satisfaction Problem
TLDR
The results endorse the well-known fact from classical CSPs that the complexity of fixed-template computational problems depends on the template’s invariance under certain operations, and show that DCSP(Γ) is polynomial-time tractable if and only if Γ is invariant under symmetric polymorphisms of all arities.
The (Coarse) Fine-Grained Structure of NP-Hard SAT and CSP Problems
TLDR
This work finds the first example of an NP-complete SAT problem with a non-trivial algorithm which also admits aNon-Trivial lower bound under SETH, and suggests a dichotomy conjecture with a close connection to the CSP dichotomy theorem.
On the complexity of CSP-based ideal membership problems
TLDR
A variation of the IMP is introduced and a unified framework, different from the celebrated Buchberger’s algorithm, is proposed to construct a bounded degree Gröbner Basis for many combinatorial problems.
A dichotomy theorem for nonuniform CSPs simplified
TLDR
The Dichotomy Conjecture for the non-uniform CSP states that for every constraint language G the problem CSP(G) is either solvable in polynomial time or is NP-complete.
Minimal Taylor Algebras as a Common Framework for the Three Algebraic Approaches to the CSP
TLDR
The theory initiated in this paper will eventually result in a simple and more natural proof of the Dichotomy Theorem that employs a simpler and more efficient algorithm, and will help in attacking complexity questions in other CSP-related problems.
A Dichotomy Theorem for Nonuniform CSPs
  • A. Bulatov
  • Mathematics
    2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2017
TLDR
The Dichotomy Conjecture for the non-uniform CSP states that for every constraint language \Gm the problem CSP is either solvable in polynomial time or is NP-complete.
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