Analysis of Relaxation Time in Random Walk with Jumps

TL;DR

This paper investigates how adding jumps to a random walk affects its relaxation time, showing that jumps can reduce relaxation time and improve network analysis efficiency.

Contribution

It provides theoretical conditions under which jumps decrease relaxation time in random walks, enhancing understanding of their impact on network sampling.

Findings

Jumps can significantly reduce relaxation time.

Conditions identified for when jumps improve convergence.

Enhanced network analysis performance with jumps.

Abstract

We study the relaxation time in the random walk with jumps. The random walk with jumps combines random walk based sampling with uniform node sampling and improves the performance of network analysis and learning tasks. We derive various conditions under which the relaxation time decreases with the introduction of jumps.