Comparative study of random walks with one-step memory on complex networks

TL;DR

This paper compares various biased random walk strategies with one-step memory on complex networks, analyzing their efficiency in search tasks through theoretical and numerical methods, and demonstrating improved search times with combined biases.

Contribution

It introduces a comprehensive analysis of biased random walks with one-step memory on complex networks, including new strategies and their combined effects on search efficiency.

Findings

Biasing based on inverse degree reduces search times.

Combining different biasing strategies enhances robustness.

Theoretical and numerical results confirm improved efficiency.

Abstract

We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph mean first passage times as an indicator for the searching efficiency. The experiments with generated and real networks show that biasing based on inverse degree, persistence and local two-hop paths can lead to smaller searching times. Moreover, these biasing approaches can be combined to achieve a more robust random search strategy. Our findings can be applied in the modeling and solution of various real-world problems.