Spectrum Assignment in Rings with Shortest-Path Routing: Complexity and Approximation Algorithms

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.