Locked constraint satisfaction problems

TL;DR

This paper introduces the class of random 'locked' constraint satisfaction problems, highlighting their complex clustered phase and extreme algorithmic hardness, offering new benchmarks for challenging optimization tasks.

Contribution

It defines and analyzes 'locked' CSPs, revealing their clustered phase and providing insights into their computational hardness, along with new benchmarks for difficult problems.

Findings

Presence of a broad clustered phase in locked CSPs

Standard algorithms fail in the clustered phase

Provides new benchmarks for hard optimization problems

Abstract

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 can be found easily, these problems, in their clustered phase, are extremely hard from the algorithmic point of view: the best known algorithms all fail to find solutions. We thus propose new benchmarks of really hard optimization problems and provide insight into the origin of their typical hardness.