We present a theoretical study of the routing and spectrum assignment (RSA) problem in ring networks. We first show that the RSA problem with fixed-alternate routing in general-topology (mesh) networks (and, hence, in rings as well) is a special case of a multiprocessor scheduling problem. We then consider bidirectional ring networks and investigate two problems: 1) the spectrum assignment problem under the assumption that each demand is routed along a single fixed path (e.g., the shortest path), and 2) the general case of the RSA problem whereby a routing decision along the clockwise and counter-clockwise directions must be made jointly with spectrum allocation. Based on insights from multiprocessor scheduling theory, we derive the complexity of the two problems and develop new constant-ratio approximation algorithms with a ratio that is strictly smaller than the best known ratio to date.
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