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Sparse linear arrays (SLAs) provide a high number of degrees of freedom (DOF) and reduce the mutual coupling effect between sensors of the array. Many design methods for SLAs have been proposed in the last two decades but most of the existing SLA design methods fail to achieve minimum number of sensors for a desired DOF. In this paper, a design method is proposed which utilizes the branch and bound (B & B) optimization algorithm to give a SLA with the desired DOF and minimum number of physical sensors. The proposed SLA design method is obtained by generalizing the minimum sensor array (MSA) design method which is recently proposed in the literature. This generalized method provides the same DOF as the MSA method but with a smaller number of physical sensors. In addition, a version of this design method is proposed which provides more robustness against mutual coupling effect between the sensors of the array. Simulation results demonstrate the superiority of the performance of the SLAs obtained with the proposed method over the arrays obtained with the MSA method and also over the other existing SLAs. [ABSTRACT FROM AUTHOR]