Notions of Connectivity in Overlay Networks

TL;DR

This paper explores different notions of connectivity in multi-layer overlay networks, demonstrating computational complexities and providing methods to compute or approximate these connectivity measures.

Contribution

It introduces a model for analyzing three connectivity notions in multi-layer networks and shows that one can be computed efficiently while providing an approximation method for network construction.

Findings

One connectivity notion can be computed in polynomial time.

Two notions are hard to compute or approximate.

An approximation method for constructing well-connected overlay networks is developed.

Abstract

" How well connected is the network? " This is one of the most fundamental questions one would ask when facing the challenge of designing a communication network. Three major notions of connectivity have been considered in the literature, but in the context of traditional (single-layer) networks, they turn out to be equivalent. This paper introduces a model for studying the three notions of connectivity in multi-layer networks. Using this model, it is easy to demonstrate that in multi-layer networks the three notions may differ dramatically. Unfortunately, in contrast to the single-layer case, where the values of the three connectivity notions can be computed efficiently, it has been recently shown in the context of WDM networks (results that can be easily translated to our model) that the values of two of these notions of connectivity are hard to compute or even approximate in multi-layer networks. The current paper shed some positive light into the multi-layer connectivity topic: we show that the value of the third connectivity notion can be computed in polynomial time and develop an approximation for the construction of well connected overlay networks.