Parallel dynamic programming algorithms

  • Marinus Veldhorst
Nonnumerical Algorithms (Session 5.2)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 237)


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(n3) time or, if the quadrangle inequality holds (cf. [7]), in O(n2) time. For the former we design parallel algorithms that run in O(n3/p) time on p<n2 processing elements (PEs). It is also shown that dynamic programming problems satisfying the quadrangle inequality can be solved in O(n2/p+n log p) time using p (1<pn) 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 (n2) PEs.


Dynamic Programming Parallel Algorithm Shared Memory Optimal Cost Systolic Array 
These 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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Marinus Veldhorst
    • 1
  1. 1.Department of Computer ScienceUniversity of UtrechtUtrechtThe Netherlands

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