Distributed scheduling algorithms for wavelength convertible WDM optical interconnects

Optical communication is attracting more and more attention because of its huge bandwidth to meet the ever increasing demand of emerging computing/networking applications. In this paper we study distributed scheduling algorithms to resolve output contentions in WDM optical interconnects with wavelength conversion ability. We consider the general case of limited range wavelength conversion, including the full range wavelength conversion. Two types of limited range wavelength conversions, circular symmetrical and non circular symmetrical, are studied. We introduce the request graph and show that finding the largest group of contention-free connection requests to achieve maximum network throughput is equivalent to finding a maximum matching in the request graph. Compared with the existing algorithm for finding a maximum matching in an arbitrary bipartite graph with time complexity O(N/sup 3/2/ k /sup 3/2/d), the algorithms we present have time complexity of O(k) and O(dk) (independent of interconnect size N) for non-circular symmetrical and circular symmetrical wavelength conversion, respectively, where k is the number of wavelengths per fiber and d is the conversion degree. In addition, our algorithms can be easily implemented in hardware, and used for time slotted WDM optical interconnects where connections hold for different number of time slots.