Evolutionary Construction of Geographical Networks with Nearly Optimal Robustness and Efficient Routing Properties

TL;DR

This paper presents a method for evolving geographical networks that balance robustness and routing efficiency by combining spatially-aware design, low-degree connectivity, and shortcut links, suitable for wide-area ad-hoc networks.

Contribution

It introduces a novel evolutionary approach incorporating spatial heterogeneity, low degrees, and shortcut links to enhance network robustness and routing efficiency.

Findings

Networks with trimodal low degrees show high tolerance to failures and attacks.

Adding shortcut links significantly improves robustness without increasing node degree.

Proposed strategies are practical for designing future wide-area ad-hoc communication networks.

Abstract

Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property, we investigate such a design from the following viewpoints: 1) network evolution according to a spatially heterogeneous population, 2) trimodal low degrees for the tolerant connectivity against both failures and attacks, and 3) decentralized routing within short paths. Furthermore, we point out the weakened tolerance by geographical constraints on local cycles, and propose a practical strategy by adding a small fraction of shortcut links between randomly chosen nodes in order to improve the robustness to a similar level to that of the optimal bimodal networks with a larger degree $O(\sqrt{N})$ for the network size $N$. These properties will be useful for constructing future ad-hoc networks in wide-area communications.