### Abstract

We show that for any odd k and any instance = of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a 1/2 +Ω (1/√ D) fraction of ß's constraints, where D is a bound on the number of constraints that each variable occurs in. This improves both qualitatively and quantitatively on the recent work of Farhi, Goldstone, and Gutmann (2014), which gave a quantum algorithm to find an assignment satisfying a 1/2 +Ω (D^{-3/4}) fraction of the equations. For arbitrary constraint satisfaction problems, we give a similar result for "triangle-free" instances; i.e., an efficient algorithm that finds an assignment satisfying at least a μ + Ω (1/√ D) fraction of constraints, where μ is the fraction that would be satisfied by a uniformly random assignment.

Original language | English (US) |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 18th International Workshop, APPROX 2015, and 19th International Workshop, RANDOM 2015 |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Pages | 110-123 |

Number of pages | 14 |

Volume | 40 |

ISBN (Print) | 9783939897897 |

DOIs | |

State | Published - Aug 1 2015 |

Event | 18th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2015, and 19th International Workshop on Randomization and Computation, RANDOM 2015 - Princeton, United States Duration: Aug 24 2015 → Aug 26 2015 |

### Other

Other | 18th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2015, and 19th International Workshop on Randomization and Computation, RANDOM 2015 |
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Country | United States |

City | Princeton |

Period | 8/24/15 → 8/26/15 |

### Fingerprint

### Keywords

- Advantage over random
- Bounded degree
- Constraint satisfaction problems

### ASJC Scopus subject areas

- Software

### Cite this

*Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 18th International Workshop, APPROX 2015, and 19th International Workshop, RANDOM 2015*(Vol. 40, pp. 110-123). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2015.110

**Beating the random assignment on constraint satisfaction problems of bounded degree.** / Barak, Boaz; Moitra, Ankur; O'Donnell, Ryan; Raghavendra, Prasad; Regev, Oded; Steurer, David; Trevisan, Luca; Vijayaraghavan, Aravindan; Witmer, David; Wright, John.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 18th International Workshop, APPROX 2015, and 19th International Workshop, RANDOM 2015.*vol. 40, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, pp. 110-123, 18th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2015, and 19th International Workshop on Randomization and Computation, RANDOM 2015, Princeton, United States, 8/24/15. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2015.110

}

TY - GEN

T1 - Beating the random assignment on constraint satisfaction problems of bounded degree

AU - Barak, Boaz

AU - Moitra, Ankur

AU - O'Donnell, Ryan

AU - Raghavendra, Prasad

AU - Regev, Oded

AU - Steurer, David

AU - Trevisan, Luca

AU - Vijayaraghavan, Aravindan

AU - Witmer, David

AU - Wright, John

PY - 2015/8/1

Y1 - 2015/8/1

N2 - We show that for any odd k and any instance = of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a 1/2 +Ω (1/√ D) fraction of ß's constraints, where D is a bound on the number of constraints that each variable occurs in. This improves both qualitatively and quantitatively on the recent work of Farhi, Goldstone, and Gutmann (2014), which gave a quantum algorithm to find an assignment satisfying a 1/2 +Ω (D-3/4) fraction of the equations. For arbitrary constraint satisfaction problems, we give a similar result for "triangle-free" instances; i.e., an efficient algorithm that finds an assignment satisfying at least a μ + Ω (1/√ D) fraction of constraints, where μ is the fraction that would be satisfied by a uniformly random assignment.

AB - We show that for any odd k and any instance = of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a 1/2 +Ω (1/√ D) fraction of ß's constraints, where D is a bound on the number of constraints that each variable occurs in. This improves both qualitatively and quantitatively on the recent work of Farhi, Goldstone, and Gutmann (2014), which gave a quantum algorithm to find an assignment satisfying a 1/2 +Ω (D-3/4) fraction of the equations. For arbitrary constraint satisfaction problems, we give a similar result for "triangle-free" instances; i.e., an efficient algorithm that finds an assignment satisfying at least a μ + Ω (1/√ D) fraction of constraints, where μ is the fraction that would be satisfied by a uniformly random assignment.

KW - Advantage over random

KW - Bounded degree

KW - Constraint satisfaction problems

UR - http://www.scopus.com/inward/record.url?scp=84958520302&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958520302&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.APPROX-RANDOM.2015.110

DO - 10.4230/LIPIcs.APPROX-RANDOM.2015.110

M3 - Conference contribution

AN - SCOPUS:84958520302

SN - 9783939897897

VL - 40

SP - 110

EP - 123

BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 18th International Workshop, APPROX 2015, and 19th International Workshop, RANDOM 2015

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -