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Routing in a wavelength-routed network can be static or dynamic. In static routing, routes for each source-destination pair in a network are predetermined, whereas in dynamic routing, a route is computed dynamically for a connection request as it arrives in the network. Dynamic routing incorporates current network state in path computation to ensure an optimal path selection. In this paper, we propose an adaptive routing algorithm, a dynamic k-routing algorithm that computes a least cost path for a connection request. The algorithm computes at most k paths before a connection request is blocked. This paper assumes no wavelength conversion in the network and that the link state information is available to each node in the network. We compare the blocking performance of the proposed adaptive routing algorithm with fixed shortest path routing, fixed alternate shortest path routing and dynamic routing (using the shortest path with available capacity) and show that this algorithm performs better in terms of blocking probability and network utilization.