A mapping procedure for synthesizing uniform recurrence equations from the dynamic programming formulation of the knapsack problem is proposed. Two new systolic arrays are synthesized from the systems of recurrence equations produced. One of these arrays is optimal with respect to both speedup and efficiency and requiresO( nb/q + n − n/q)time andO( q[wmax/2]) processors, wherebis the knapsack capacity,nis the number of items,wmaxis the maximum weight taken over all items, andq > 0 is an arbitrary chosen design parameter.