Enhanced Random Walk with Choice: An Empirical Study

TL;DR

This paper introduces an enhanced random walk with choice that considers neighborhood visit intensity, leading to improved cover time and load balancing in random geometric graphs.

Contribution

It proposes a new metric for the random walk with choice, incorporating neighborhood visit intensity, and demonstrates its effectiveness through simulation.

Findings

Significant improvement in cover time

Reduced maximum node load

Better load balancing in geometric graphs

Abstract

The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number of (past) visits of the walk to the node. In this paper we propose an enhancement to the random walk with choice by considering a new metric that captures not only the actual visits to a given node, but also the intensity of the visits to the neighbourhood of the node. We compare the random walk with choice with its enhanced counterpart. Simulation results show a significant improvement in cover time, maximum node load and load balancing, mainly in random geometric graphs.