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This paper addresses the joint relay assignment and power allocation problem for orthogonal multiuser systems using amplify-and-forward (AF) relaying nodes in the downlink. Our aim is to maximize the sum-rate subject to individual and total power constraints on the relays and a relay assignment constraint. In the case of fixed relay selection, the power allocation optimization is convex and an efficient recursive algorithm is proposed to achieve the optimum. The joint optimization of relay selection and power allocation, however, appears to be non-convex and is not known to be tractable. To tackle this, we propose a novel algorithm using Markov chain Monte-Carlo with Kullback-Leibler divergence minimization (MCMC-KLDM), which is proved to converge to the global optimum almost surely. Results show that the proposed scheme significantly outperforms a greedy approach and achieves near-optimal performance at very low complexity.