Scalable Node-Disjoint and Edge-Disjoint Multi-wavelength Routing

Probabilistic message-passing algorithms are developed for routing transmissions in multi-wavelength optical communication networks, under node and edge-disjoint routing constraints and for various objective functions. Global routing optimization is a hard computational task on its own but is made much more difficult under the node/edge-disjoint constraints and in the presence of multiple wavelengths, a problem which dominates routing efficiency in real optical communication networks that carry most of the world's Internet traffic. The scalable principled method we have developed is exact on trees but provides good approximate solutions on locally tree-like graphs. It accommodates a variety of objective functions that correspond to low latency, load balancing and consolidation of routes, and can be easily extended to include heterogeneous signal-to-noise values on edges and a restriction on the available wavelengths per edge. It can be used for routing and managing transmissions on existing topologies as well as for designing and modifying optical communication networks. Additionally, it provides the tool for settling an open and much debated question on the merit of wavelength-switching nodes and the added capabilities they provide. The methods have been tested on generated networks such as random-regular, Erd\H{o}s R\'{e}nyi and power-law graphs, as well as on the UK and US optical communication networks. They show excellent performance with respect to existing methodology on small networks and have been scaled up to network sizes that are beyond the reach of most existing algorithms.