License
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.110
URN: urn:nbn:de:0030-drops-52981
URL: http://drops.dagstuhl.de/opus/volltexte/2015/5298/
Go to the corresponding LIPIcs Volume Portal


Barak, Boaz ; Moitra, Ankur ; O’Donnell, Ryan ; Raghavendra, Prasad ; Regev, Oded ; Steurer, David ; Trevisan, Luca ; Vijayaraghavan, Aravindan ; Witmer, David ; Wright, John

Beating the Random Assignment on Constraint Satisfaction Problems of Bounded Degree

pdf-format:
8.pdf (0.5 MB)


Abstract

We show that for any odd k and any instance I of the max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a 1/2 + Omega(1/sqrt(D)) fraction of I'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 Omega(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 mu + Omega(1/sqrt(degree)) fraction of constraints, where mu is the fraction that would be satisfied by a uniformly random assignment.

BibTeX - Entry

@InProceedings{barak_et_al:LIPIcs:2015:5298,
  author =	{Boaz Barak and Ankur Moitra and Ryan O’Donnell and Prasad Raghavendra and Oded Regev and David Steurer and Luca Trevisan and Aravindan Vijayaraghavan and David Witmer and John Wright},
  title =	{{Beating the Random Assignment on Constraint Satisfaction Problems of Bounded Degree}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{110--123},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Naveen Garg and Klaus Jansen and Anup Rao and Jos{\'e} D. P. Rolim},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5298},
  URN =		{urn:nbn:de:0030-drops-52981},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.110},
  annote =	{Keywords: constraint satisfaction problems, bounded degree, advantage over random}
}

Keywords: constraint satisfaction problems, bounded degree, advantage over random
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)
Issue Date: 2015
Date of publication: 28.07.2015


DROPS-Home | Fulltext Search | Imprint Published by LZI