p-cycle network design: From fewest in number to smallest in size

An idea seems to have spread that p-cycle networks are always based on a single Hamiltonian cycle. The correct understanding is that while they can be based on a Hamiltonian, network designs involving multiple p-cycles are far more capacity-efficient in general. In fact, from an optical networking standpoint one would probably like to work with p-cycles of the smallest size (circumference) possible, to satisfy optical reach considerations, and in this case the number of p-cycles might be even more numerous than a pure minimum capacity design. However, the fact that an entire network could be protected by a single cyclic structure could be attractive from another viewpoint simply because only one logical structure has to be managed. Thus, different recent orientations have brought us to realize the need for a study of p-cycle network designs that vary systematically across the range between the smallest size p-cycles, to using the fewest number of p-cycles. Questions include: What are the design models for p-cycle networks that use the fewest number of distinct structures? What are the capacity implications of a design restricted to a specific maximum number of structures? Can a capacity-optimal design be ¿nudged¿ into using fewer structures in total without requiring any extra capacity? What happens to the number of structures if the smallest possible p-cycles are insisted upon? Accordingly, we offer a systematic study of the optimal p-cycle network design problem addressing such questions about how the logical number of p-cycle structures present or allowed in a design interacts with the minimum spare capacity required for the design to be 100% restorable.