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A numerically-efficient technique based on the Bayesian compressive sampling (BCS) for the design of maximally-sparse linear arrays is introduced. The method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine (RVM) for the problem solution. The proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non-uniformly spaced active elements. The numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state-of-the-art techniques for the design of sparse arrays.