ﻻ يوجد ملخص باللغة العربية
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 $frac{1}{2} + Omega(1/sqrt{D})$ fraction of 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 emph{quantum} algorithm to find an assignment satisfying a $frac{1}{2} + Omega(D^{-3/4})$ 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 $mu + Omega(1/sqrt{D})$ fraction of constraints, where $mu$ is the fraction that would be satisfied by a uniformly random assignment.
We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase diagram in te
We prove super-polynomial lower bounds on the size of linear programming relaxations for approximati
The set of solutions of random constraint satisfaction problems (zero energy groundstates of mean-field diluted spin glasses) undergoes several structural phase transitions as the amount of constraints is increased. This set first breaks down into a
The typical complexity of Constraint Satisfaction Problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a clustering or
We introduce and study the random locked constraint satisfaction problems. When increasing the density of constraints, they display a broad clustered phase in which the space of solutions is divided into many isolated points. While the phase diagram