Spectrum assignment in rings with shortest-path routing: Complexity and approximation algorithms

Abstract

Abstract-We study the spectrum assignment (SA) problem in ring networks with shortest path (or, more generally, fixed) routing. With fixed routing, each traffic demand follows a predetermined path to its destination. In earlier work, we have shown that the SA problem can be viewed as a multiprocessor problem. Based on this insight, we prove that, under the shortest path assumption, the SA problem can be solved in polynomial time in small rings, and we develop constant-ratio approximation algorithms for large rings. For rings of size up to 16 nodes (the maximum size of a SONET/SDH ring), the approximation ratios of our algorithms are strictly smaller than the best known ratio to date.

Spectrum Assignment in Optical Networks: A Multiprocessor Scheduling Perspective

“…We then carry out an in-depth study of the SA problem in chain (linear) networks and develop constant-ratio approximation algorithms and heuristics that are inspired by the new scheduling perspective. In addition to advancing our understanding of SA as a scheduling problem, our new results are important in that 1) they can be readily extended to ring networks that comprise large parts of the existing optical network infrastructure, as we have shown in more recent work [18]; 2) they may be used to analyze approximately general-topology networks, e.g., by extending path-based decomposition techniques that have been developed for the more special case of wavelength assignment [19]; and 3) they may be applied to solve large-scale multiprocessor scheduling problems efficiently and effectively, as our numerical results demonstrate.…”