Phase Transitions and Computational Difficulty in Random Constraint Satisfaction Problems

TL;DR

This paper reviews the phase transitions and computational challenges in random constraint satisfaction problems, especially q-coloring of large random graphs, using insights from physics and the cavity method.

Contribution

It provides a comprehensive overview of the phase diagram, glass transition phenomena, and algorithmic difficulties in random CSPs based on physics-inspired methods.

Findings

Identification of phase transition points in graph coloring

Connection between phase transitions and computational hardness

Insights into the glass transition phenomenology in CSPs

Abstract

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 temperature, the connections with the glass transition phenomenology in physics, and the related algorithmic issues.