A systolic algorithm for dynamic programming

Abstract

We present a formal systolic algorithm to solve the dynamic programming problem for an optimal binary search tree. For a fixed integer j such that 2 ≤ j ≤ n, first we derive a linear systolic array to evaluate the minimal cost c_i,j for 1 ≤ i < j. Then we combine these (n − 1) linear systolic arrays to form a two-dimensional systolic array. The computational model consists of ⌈(n² + 2n − 4)/4⌉ processing elements. The algorithm requires (2n − 3) time steps to solve this problem. The elapsed time within a time step is independent of the problem size n. It is suitable for the VLSI implementation due to the identical and simple structure of processing elements. We also prove the correctness of this algorithm by induction.