Bicoloring Random Hypergraphs

TL;DR

This paper investigates the bicoloring problem in random hypergraphs using analytical and numerical methods, identifying phase transitions and testing algorithms in challenging instances.

Contribution

It applies the zero-temperature cavity method and Survey Propagation to analyze phase transitions and algorithm performance in bicoloring hypergraphs.

Findings

Analytical phase transition points agree with numerical results.

Survey Propagation effectively handles HARD-SAT instances.

Identifies dynamic and static phase transitions in the problem.

Abstract

We study the problem of bicoloring random hypergraphs, both numerically and analytically. We apply the zero-temperature cavity method to find analytical results for the phase transitions (dynamic and static) in the 1RSB approximation. These points appear to be in agreement with the results of the numerical algorithm. In the second part, we implement and test the Survey Propagation algorithm for specific bicoloring instances in the so called HARD-SAT phase.