Comparison of p-cycles and p-trees in a unified mathematical framework

Abstract

As high-speed networks grow in capacity, network protection becomes increasingly important. Recently, following interest in p-cycle protection, the related concept of p-trees has also been studied. In one line of work, a so-called “hierarchical tree” approach is studied and compared to p-cycles on some points. Some of the qualitative conclusions drawn, however, apply only to p-cycle designs consisting of a single Hamiltonian p-cycle. There are other confounding factors in the comparison between the two, such as the fact that, while the tree-based approach is not 100% restorable, p-cycles are. The tree and p-cycle networks are also designed by highly dissimilar methods. In addition, the claims regarding hierarchical trees seem to contradict earlier work, which found pre-planned trees to be significantly less capacity-efficient than p-cycles. These contradictory findings need to be resolved; a correct understanding of how these two architectures rank in terms of capacity efficiency is a basic issue of network science in this field. We therefore revisit the question in a definitive and novel way in which a unified optimal design framework compares minimum capacity, 100% restorable p-tree and p-cycle network designs. Results confirm the significantly higher capacity efficiency of p-cycles. Supporting discussion provides intuitive appreciation of why this is so, and the unified design framework contributes a further theoretical appreciation of how pre-planned trees and pre-connected cycles are related. In a novel further experiment we use the common optimal design model to study p-cycle/p-tree hybrid designs. This experiment answers the question “To what extent can a selection of trees compliment a cycle-based design, or vice-versa?” The results demonstrate the intrinsic merit of cycles over trees for pre-planned protection.