Parallel dynamic programming algorithms

Abstract

This paper presents a number of parallel algorithms for the dynamic programming problem $$\begin{gathered}c(i,i) = 0 (0 \leqslant i \leqslant n) \hfill \\\mathop {c(i,j) = w(i,j) + \min (c(i,m - 1) + c(m,j))}\limits_{i < m \leqslant j} \hfill \\\end{gathered} $$ Sequential algorithms run in O(n 3) time or, if the quadrangle inequality holds (cf. [7]), in O(n 2) time. For the former we design parallel algorithms that run in O(n 3/p) time on p<n 2 processing elements (PEs). It is also shown that dynamic programming problems satisfying the quadrangle inequality can be solved in O(n 2/p+n log p) time using p (1<p≤n) PEs. A global shared memory is assumed. Moreover, we design a systolic array for computing the c(i,j)'s that runs in linear time using p (n 2) PEs.KeywordsDynamic ProgrammingParallel AlgorithmShared MemoryOptimal CostSystolic ArrayThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.