An efficient parallel dynamic programming algorithm

Antonio, Tsai, and Huang proposed a scheme in 1991 to parallelize the standard dynamic programming approach to solve combinatorial multistage problems. However, their dynamic programming approach is restricted to those multistage problems where the decision made at each stage depends only on decisions made in the stage immediately preceding it. For many interesting problems the decision at each stage depends on the decisions made at all the previous stages, and therefore their approach doesnʹt apply. The Matrix Chain Multiplication problem, Longest Common Subsequence problem, and Optimal Polygon Triangulation problem are some examples of such problems. We also present techniques for parallelizing the dynamic programming solution to such problems. The parallel algorithm we develop for a PRAM has complexity θ(n) employing θ(n2) processors. Since the traditional sequential algorithm for such problems is θ(n3), our parallel algorithm is an optimal parallel algorithm based on this traditional algorithm. We also describe the results of our experiments that are in conformity with our theoretical complexity results. We also compare and contrast our result with results obtained by earlier researchers and show that our parallel algorithm has optimal efficiency of 100% with respect to the traditional Dynamic Programming Algorithm.