On a cover time problem on a dynamic graph with steps at random times

TL;DR

This paper studies the time it takes for a random walk to cover all nodes in a dynamic graph that expands over time, analyzing cover time and return statistics in a novel evolving graph model.

Contribution

It introduces a new cover time problem for random walks on expanding dynamic graphs with random movement times, providing initial analysis of cover and return times.

Findings

Analysis of cover time in dynamic expanding graphs

Results on the number of returns to initial states

Insights into random walk behavior on evolving networks

Abstract

We introduce a cover time problem for random walks on dynamic graphs in which the graph expands in time and the walker moves at random times. Time to cover all nodes and number of returns to original states are analyzed in resulting model.