Routing and wavelength assignment in all-optical wdm wavelength-routing networks

Many technologies exist to improve the network communications capabilities that are available to users. Gigabit bitrates, low propagation latency, and low error rates are among the bandwidth enhancements provided by optical networks. By spatially partitioning the fiber bandwidth into distinct parallel optical channels, wavelength division multiplexing (WDM) enables the efficient use of optical resources. By combining WDM with passive or active wavelength selective switches, a variety of wavelength-routing network topologies may be realized. This dissertation first addresses the computational complexity of finding the optimal number of wavelengths for tree and mesh network topologies. The problem of determining the optimal number of wavelengths needed for any set of connection requests on directed rectangular meshes that use arbitrary routing is considered in detail. This problem is shown to be NP-complete, leading to the conclusion that approximation algorithms achieving constant bounded performance for this problem do not exist. Attention is then focused on the important problem of finding algorithms for wavelength assignment on several industrially relevant topologies. Optimal algorithms for undirected trees and directed stars are developed, and hypergraph theory is used to define a class of communication requests on directed trees that results in a 3/2 optimal approximation algorithm. A twice-optimal approximation algorithm for wavelength assignment in directed meshes is given, with some restrictions on path adjacency. An algorithm for 12/7 optimal wavelength assignment for all-to-all gossiping, a data distribution technique that is of interest to parallel algorithm designers, on square meshes using row-column routing is developed and analyzed. Results on bounded resource allocation are also demonstrated for all-to-all gossiping on square meshes. Finally, the applied problem of transferring files in optical networks is examined. Lower bounds for the lengths of transfer schedules are found, and it is shown that calculating the optimal schedule is NP-complete. Approximation algorithms for scheduling 2-hop file transfers are developed under various network topologies. The techniques used for these algorithms are applied to the WAP. Assignment algorithms that perform to within $L\sb{max}+1$ and $3L\sb{max}/2$ are then developed for unique and non-unique connection requests, respectively. The computational complexity results presented in this dissertation contribute to the theoretical foundations of the emerging advanced technology of wavelength-routing WDM networking and extend previous results on wavelength assignment. The algorithms, both optimal and approximation, provide critical components for the control and management of important network topologies and improve existing results in routing and wavelength assignment.