In this paper, we explore the routing and wavelength assignment problem for the CBT service in a WDM network where k sources need to send data to a common core node. We formally model the problem as a problem of finding k shortest lightpaths from sources to the core subject to the constraint of wavelength collision free. We define and study several subproblems, each addressing a different objective. For the feasibility and the minimum total cost problems of k shortest lightpaths, we show how the classical network flow algorithms can be modified and applied efficiently on the network flow model constructed on the transformed wave-length graph. For the minimum max-cost problem, we prove its NP-completeness and propose two efficient heuristic algorithms. Simulation results show that the proposed heuristic algorithms perform very close to the calculated lower bounds.