The Minimum Number of Hubs in Networks

TL;DR

This paper investigates the minimum number of hubs required in a network to satisfy flow demands between multiple source-sink pairs, providing tight bounds and a novel path-searching algorithm for specific cases.

Contribution

It establishes upper bounds on the number of hubs needed and introduces a new path-searching algorithm for networks with two source-sink pairs.

Findings

The minimum number of hubs is always upper bounded regardless of network size or topology.

Tight upper bounds are derived for certain network parameters.

A novel path-searching algorithm is developed for networks with two source-sink pairs.

Abstract

In this paper, a hub refers to a non-terminal vertex of degree at least three. We study the minimum number of hubs needed in a network to guarantee certain flow demand constraints imposed between multiple pairs of sources and sinks. We prove that under the constraints, regardless of the size or the topology of the network, such minimum number is always upper bounded and we derive tight upper bounds for some special parameters. In particular, for two pairs of sources and sinks, we present a novel path-searching algorithm, the analysis of which is instrumental for the derivations of the tight upper bounds.