A note on hierarchical hubbing for a generalization of the VPN problem

TL;DR

This paper demonstrates that the optimal hierarchical hubbing solution for a generalized VPN problem can be computed efficiently, extending the applicability of hierarchical hubbing in robust network design.

Contribution

It proves the polynomial-time computability of optimal hierarchical hubbing solutions for a broad generalization of the VPN problem.

Findings

Optimal hierarchical hubbing solutions can be found efficiently.

Extends hierarchical hubbing applicability to new VPN generalizations.

Supports a generalized VPN Conjecture.

Abstract

Robust network design refers to a class of optimization problems that occur when designing networks to efficiently handle variable demands. The notion of "hierarchical hubbing" was introduced (in the narrow context of a specific robust network design question), by Olver and Shepherd [2010]. Hierarchical hubbing allows for routings with a multiplicity of "hubs" which are connected to the terminals and to each other in a treelike fashion. Recently, Fr\'echette et al. [2013] explored this notion much more generally, focusing on its applicability to an extension of the well-studied hose model that allows for upper bounds on individual point-to-point demands. In this paper, we consider hierarchical hubbing in the context of a previously studied (and extremely natural) generalization of the hose model, and prove that the optimal hierarchical hubbing solution can be found efficiently. This result is relevant to a recently proposed generalization of the "VPN Conjecture".