Average-case complexity of a branch-and-bound algorithm for maximum independent set, under the $\mathcal{G}(n,p)$ random model

TL;DR

This paper analyzes the average-case complexity of a branch-and-bound algorithm for maximum independent set in random graphs, identifying phase transitions between subexponential and exponential complexities based on edge probability.

Contribution

It provides a detailed phase transition analysis of the algorithm's complexity in the $\, ext{G}(n,p)$ random graph model, highlighting how complexity varies with edge probability.

Findings

Identifies phase transitions between subexponential and exponential complexities.

Provides precise analysis of average-case complexity depending on $p$.

Highlights the impact of edge probability on algorithm performance.

Abstract

We study average-case complexity of branch-and-bound for maximum independent set in random graphs under the $\mathcal{G}(n,p)$ distribution. In this model every pair $(u,v)$ of vertices belongs to $E$ with probability $p$ independently on the existence of any other edge. We make a precise case analysis, providing phase transitions between subexponential and exponential complexities depending on the probability $p$ of the random model.