# Evolutionary Construction of Geographical Networks with Nearly Optimal Robustness and Efficient Routing Properties - Physics > Data Analysis, Statistics and Probability

Abstract: Robust and efficient design of networks on a realistic geographical space isone of the important issues for the realization of dependable communicationsystems.
In this paper, based on a percolation theory and a geometric graphproperty, we investigate such a design from the following viewpoints: 1network evolution according to a spatially heterogeneous population, 2trimodal low degrees for the tolerant connectivity against both failures andattacks, and 3 decentralized routing within short paths.
Furthermore, we pointout the weakened tolerance by geographical constraints on local cycles, andpropose a practical strategy by adding a small fraction of shortcut linksbetween randomly chosen nodes in order to improve the robustness to a similarlevel to that of the optimal bimodal networks with a larger degree$O\sqrt{N}$ for the network size $N$.
These properties will be useful forconstructing future ad-hoc networks in wide-area communications.

Author: Yukio Hayashi

Source: https://arxiv.org/