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Towards a characterization of constant-factor approximable finite-valued CSPsOpen Access

Published in Academic Press Inc.

2018

Volume: 97

Pages: 14 - 27

We study the approximability of (Finite-)Valued Constraint Satisfaction Problems (VCSPs) with a fixed finite constraint language Γ consisting of finitary functions on a fixed finite domain. Ene et al. have shown that, under a mild technical condition, the basic LP relaxation is optimal for constant-factor approximation for VCSP(Γ) unless the Unique Games Conjecture fails. Using the algebraic approach to the CSP, we give new natural algebraic conditions for the finiteness of the integrality gap for the basic LP relaxation of VCSP(Γ) and show how this leads to efficient constant-factor approximation algorithms for several examples that cover all previously known cases that are NP-hard to solve to optimality but admit constant-factor approximation. Finally, we show that the absence of another algebraic condition leads to NP-hardness of constant-factor approximation. Thus, our results indicate where the boundary of constant-factor approximability for VCSPs lies. © 2018 Elsevier Inc.

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About the journal

Journal | Journal of Computer and System Sciences |
---|---|

Publisher | Academic Press Inc. |

ISSN | 00220000 |

Open Access | Yes |

Concepts (13)

- Algebra
- Approximation algorithms
- Constraint theory
- Optimization
- ALGEBRAIC APPROACHES
- Algebraic conditions
- CONSTANT FACTOR APPROXIMATION
- CONSTANT-FACTOR APPROXIMABILITY
- Constant-factor approximation algorithms
- UNIQUE GAMES CONJECTURE
- UNIVERSAL ALGEBRA
- VALUED CONSTRAINT SATISFACTION PROBLEMS
- Constraint satisfaction problems