On the PVM/MPI computations of dynamic programming recurrences

Abstract

We investigate distributed parallel computation of a general dynamic programming problem given by a class of dynamic programming recurrences. Our approach is to partition the dynamic programming array into square blocks and use a kind of pipelining, instead of computing the array by diagonals, or by rows/columns, see [7]. One possibility is to make a coarse-grained implementation of systolic algorithms from [3, 4]. We choose a completely different approach and start with a new synchronous shared-memory algorithm for the problem. The fine-grained synchronous parallel computation is transformed into a coarse-grained message-passing algorithm. The dynamic programming array (usually very large) is distributed in such a way that each machine keeps only a small portion of the array and the whole array does not need to be stored in one large piece anywhere. The synchronous shared memory model is a better starting point for distributed implementation compared with any systolic algorithm (with much larger degree of synchronization), since it enables more alternative implementations. Incidentally, our approach gives also a new and simple alternative algorithm working on a mesh of processors. We discuss three alternative implementations and compare the suitability of PVM and MPI models for the problem.

Supported partially by the grant KBN 8T11C01208.