Spatial Separability in Hub Location Problems with an Application to Brain Connectivity Networks

Abstract

Motivated by the need to solve large hub location problems efficiently and accurately, we discover an important characteristic of optimal solutions to p-hub median problems that we call spatial separability. It refers to the partitioning of the network into allocation clusters with nonoverlapping convex hulls. We illustrate numerically that the property persists over a wide range of randomly generated instances and propose a data-driven approach based on an insight from the property to tackle very large problem sizes. Computational experiments corroborate the effectiveness of the proposed approach in generating high-quality solutions within reasonable computational times. We then explore a new application area of hub location problems in brain connectivity networks and introduce the largest and the first set of three-dimensional instances in the literature. Computational results demonstrate the capability of hub location models in successfully depicting the hub organization of the human brain, as validated by the medical literature, thus revealing that hub location models can play an important role in investigating the intricate connectivity of the human brain.