Local heuristics and the emergence of spanning subgraphs in complex networks

TL;DR

This paper investigates local heuristics for creating spanning subgraphs in complex networks, aiming to optimize information dissemination efficiency, resilience, and adaptability through mathematical analysis and simulations.

Contribution

It introduces and analyzes two new heuristics for spanning subgraphs, demonstrating their effectiveness in network dissemination and resilience.

Findings

Spanning subgraphs can be efficiently formed using local heuristics.

The heuristics perform well in reaching all nodes with minimal messages.

Spanning subgraphs show resilience and adaptability to network changes.

Abstract

We study the use of local heuristics to determine spanning subgraphs for use in the dissemination of information in complex networks. We introduce two different heuristics and analyze their behavior in giving rise to spanning subgraphs that perform well in terms of allowing every node of the network to be reached, of requiring relatively few messages and small node bandwidth for information dissemination, and also of stretching paths with respect to the underlying network only modestly. We contribute a detailed mathematical analysis of one of the heuristics and provide extensive simulation results on random graphs for both of them. These results indicate that, within certain limits, spanning subgraphs are indeed expected to emerge that perform well in respect to all requirements. We also discuss the spanning subgraphs' inherent resilience to failures and adaptability to topological changes.