In this paper a bidirectional linear systolic array (BLSA) that computes minimum cost spanning tree (MCST) of a given graph is designed. We present a synthesis procedure, based on data dependencies and space-time transformations of index space, to design BLSA with optimal number of processing elements (PEs) for a given problem size. The execution time is minimized for that number of PEs. Explicit mathematical formulas for systolic array synthesis are derived. We compare performances of the BLSA with the unidirectional linear systolic array (ULSA).