A general approach for all-to-all routing in multihop WDM optical networks

WDM optical networks provide unprecedented high speed and reliability for message transfer among the nodes. All-to-all routing is a fundamental routing problem in such networks and has been well studied on single hop WDM networks. However, the number of wavelengths to realize all-to-all routing on the single hop model typically is very large. One way to reduce the number of wavelengths is to use k-hop routing, in which each routing path consists of k segments and each segment is assigned a different wavelength, where k usually is a small constant. Because of the complexity of design and analysis for such a routing problem, only few papers discussed and proposed all-to-all routing by k ≥ 2 hops. However, the proposed algorithms are usually exceeding complicated even for ring topologies. Often, an ad hoc approach is employed to deal with each individual topology. In this paper we propose a generic method for all-to-all routing in multi-hop WDM networks, which aims to minimize the number of wavelengths. We illustrate the approach for several optical networks of commonly used topology, including lines, rings, tori, meshes, and complete binary trees. For each case an upper bound on the number of wavelengths is obtained. The results show that this approach produces clear routing paths, requires less wavelengths, and can easily incorporate load balancing. For simple topologies such as lines and rings, this approach easily produces the same bounds on the number of wavelengths that were hard-obtained previously. Moreover, this general approach provides a unified routing algorithm for any d-dimensional torus, which seems impossible to obtain by the previous approach.