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Optical communication is a promising candidate for many emerging networking and parallel/distributed computing applications because of its huge bandwidth. Wavelength division multiplexing (WDM) is a technique that can better utilize the optical bandwidth by dividing the bandwidth of a fiber into multiple wavelength channels. In this paper, we study optimal scheduling algorithms to resolve output contentions in bufferless time slotted WDM optical interconnects with wavelength conversion ability. We consider the general case of limited range wavelength conversion with arbitrary conversion capability, as limited range wavelength conversion is easier to implement and more cost effective than full range wavelength conversion, and it also includes full range wavelength conversion as a special case. We first consider the conversion scheme in which each wavelength can be converted to multiple wavelengths in an interval of wavelengths and the intervals for different wavelengths are "ordered". We show that the problem of maximizing network throughput can be formalized as finding a maximum matching in a bipartite graph. We then give an optimal scheduling algorithm called the first available algorithm that runs in O(k) time, where k is the number of wavelengths per fiber. We also study the case where the connection requests have different priorities. We formalize the problem as finding an optimal matching in a weighted bipartite graph and give a scheduling algorithm called the downwards expanding algorithm that runs in O(kD + Nklog(Nk)) time where N is the number of input fibers of the interconnect and D is the conversion degree. Finally, we consider the circular symmetrical wavelength conversion scheme and give optimal scheduling algorithms for nonprioritized scheduling in O(Dk) time and prioritized scheduling in O(k2+Nklog(Nk)) time.