Hiding Quiet Solutions in Random Constraint Satisfaction Problems

TL;DR

This paper investigates the properties and phase transitions of planted random constraint satisfaction problems, revealing similarities with usual ensembles and exploring their computational complexity and phase diagrams.

Contribution

It demonstrates that certain properties of standard random ensembles are preserved in planted ensembles and analyzes phase transitions and complexity patterns.

Findings

Properties of planted and usual ensembles are quantitatively similar.

Identifies the easy/hard/easy computational complexity pattern.

Explores the phase diagram with liquid, glass, and solid phases.

Abstract

We study constraint satisfaction problems on the so-called 'planted' random ensemble. We show that for a certain class of problems, e.g. graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the planted random ensemble. We study the structural phase transitions, and the easy/hard/easy pattern in the average computational complexity. We also discuss the finite temperature phase diagram, finding a close connection with the liquid/glass/solid phenomenology.