# An exact algorithm exhibiting RS-RSB/easy-hard correspondence for the maximum independent set problem

## TL;DR

This paper analyzes an exact algorithm for the maximum independent set problem, showing it outperforms simpler methods and overcomes known hardness transitions, thus providing insights into the problem's computational complexity.

## Contribution

It introduces an exact algorithm that surpasses previous methods by working beyond the core transition point and up to the RSB transition, revealing the role of RSB in problem hardness.

## Key findings

- Exponential improvement in running time in certain parameter regions
- Overcomes the core transition point where leaf removal fails
- Operates up to the RSB transition point, indicating RSB as a key obstacle

## Abstract

A recently proposed exact algorithm for the maximum independent set problem is analyzed. The typical running time is improved exponentially in some parameter regions compared to simple binary search. The algorithm also overcomes the core transition point, where the conventional leaf removal algorithm fails, and works up to the replica symmetry breaking (RSB) transition point. This suggests that a leaf removal core itself is not enough for typical hardness in the random maximum independent set problem, providing further evidence for RSB being the obstacle for algorithms in general.