The covertime of a biased random walk on $G_{n,p}$

TL;DR

This paper investigates the covertime of a biased random walk on Erdős–Rényi random graphs, showing that bias towards low-degree vertices reduces the covertime compared to unbiased walks.

Contribution

It introduces a bias towards low-degree vertices in random walks on $G_{n,p}$ and analyzes how this bias affects the covertime, providing new insights into graph exploration dynamics.

Findings

Biased walk reduces covertime compared to unbiased walk

Covertime depends on the degree distribution of the graph

Bias towards low-degree vertices accelerates coverage

Abstract

We analyze the covertime of a biased random walk on the random graph $G_{n,p}$. The walk is biased towards visiting vertices of low degree and this makes the covertime less than in the unbiased case