Lightpath arrangement in survivable rings to minimize the switching cost

This paper studies the design of low-cost survivable wavelength-division-multiplexing (WDM) networks. To achieve survivability, lightpaths are arranged as a set of rings. Arrangement in rings is also necessary to support SONET/SDH protection schemes such as 4FBLSR above the optical layer. This is expected to be the most common architecture in regional (metro) networks. We assume that we are given a set of lightpaths in an arbitrary network topology and aim at finding a partition of the lightpaths to rings adding a minimum number of lightpaths to the original set. The cost measure that we consider (number of lightpaths) reflects the switching cost of the entire network. In the case of a SONET/SDH higher layer, the number of lightpaths is equal to the number of add-drop multiplexers (ADMs) (since two subsequent lightpaths in a ring can share an ADM at the common node). We prove some negative results on the tractability and approximability of the problem and provide an approximation algorithm with a worst case approximation ratio of 8/5. We study some special cases in which the performance of the algorithm is improved. A similar problem was introduced, motivated, and studied by Liu, Li, Wan and Frieder (see Proc. INFOCOM 2000, p.1020-1025, 2000) Gerstel, Lin and Sasaki, (see Proc. IEEE INFOCOM '98, p. 94-101, 1998)(where it was termed minimum ADM problem). However, these two works focused on a ring topology while we generalize the problem to an arbitrary network topology.