Performance evaluation of a parallel dynamic programming algorithm for solving the matrix chain product problem

We address in this paper a particular combinatorial optimization problem (COP) namely the matrix chain product problem (MCPP). We particularly consider the parallelization of the dynamic programming algorithm (DPA) for solving the MCPP which is structured in a DO loop nest of depth 3. Our approach is based on a three-phase procedure. The first consists in transforming the DPA into a perfect loop nest (PLN). The second applies a dependency analysis within the initial PLN permitting the determination of the type of each loop (serial or parallel). As to the third phase, it applies on the initial PLN the loop interchange technique in order to increase the parallelism degree. We focus in this paper on an experimental study achieved on a parallel multicore machine that permits to validate our theoretical contribution.