Exploring Low-degree Nodes First Accelerates Network Exploration

TL;DR

This paper introduces the Min-degree (MD) strategy for network exploration, which biases random walks towards peripheral nodes under degree inspection constraints, and demonstrates its effectiveness through extensive benchmarking.

Contribution

It proposes a novel Partial Cover Time with Budget problem and an efficient MD strategy that improves network exploration under limited degree information.

Findings

MD strategy outperforms existing algorithms in real datasets.

Biasing towards peripheral nodes accelerates network coverage.

The approach is effective even with limited neighbor degree knowledge.

Abstract

We consider information diffusion on Web-like networks and how random walks can simulate it. A well-studied problem in this domain is Partial Cover Time, i.e., the calculation of the expected number of steps a random walker needs to visit a given fraction of the nodes of the network. We notice that some of the fastest solutions in fact require that nodes have perfect knowledge of the degree distribution of their neighbors, which in many practical cases is not obtainable, e.g., for privacy reasons. We thus introduce a version of the Cover problem that considers such limitations: Partial Cover Time with Budget. The budget is a limit on the number of neighbors that can be inspected for their degree; we have adapted optimal random walks strategies from the literature to operate under such budget. Our solution is called Min-degree (MD) and, essentially, it biases random walkers towards visiting peripheral areas of the network first. Extensive benchmarking on six real datasets proves that the---perhaps counter-intuitive strategy---MD strategy is in fact highly competitive wrt. state-of-the-art algorithms for cover.