Dominating Scale-Free Networks Using Generalized Probabilistic Methods

TL;DR

This paper introduces new probabilistic strategies for selecting dominating sets in scale-free networks, outperforming traditional methods and providing analytical bounds validated on real-world data.

Contribution

It proposes two novel probabilistic dominating set selection strategies tailored for heterogeneous networks, with one achieving minimal size and outperforming degree-based methods.

Findings

Probabilistic methods outperform deterministic degree-based approaches.

Degree-dependent probabilistic selection becomes optimal in certain limits.

Identified the threshold where high-degree node selection becomes inefficient.

Abstract

We study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for applications. We propose two novel probabilistic dominating set selection strategies that are applicable to heterogeneous networks. One of them obtains the smallest probabilistic dominating set and also outperforms the deterministic degree-ranked method. We show that a degree-dependent probabilistic selection method becomes optimal in its deterministic limit. In addition, we also find the precise limit where selecting high-degree nodes exclusively becomes inefficient for network domination. We validate our results on several real-world networks, and provide highly accurate analytical estimates for our methods.