## Abstract

The authors are concerned with dynamic programming (DP) algorithms whose solution is given by a recurrence relation similar to that for the matrix parenthesization problem. Guibas, Kung and Thompson (1979), presented a systolic array algorithm for this problem that uses O(n^{2}) processing cells and solves the problem in O(n) time. The authors present three different mappings of this systolic algorithm on a mesh connected parallel computer. The first two mappings use commonly known techniques for mapping systolic arrays to mesh computers. Both of them are able to obtain only a fraction of maximum possible performance. The primary reason for the poor performance of these formulations is that different nodes at different levels in the multistage graph in the DP formulation require different amounts of computation. Any adaptation has to take this into consideration and evenly distribute the work among the processors. The third mapping balances the work load among processors and thus is capable of providing efficiency approximately equal to 1 (i.e., speedup approximately equal to the number of processors) for any number of processors and sufficiently large problem. They experimentally evaluate these mappings on a mesh embedded onto a 256 processor nCUBE/2.

Original language | English (US) |
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Title of host publication | Proceedings of 7th International Parallel Processing Symposium, IPPS 1993 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 563-568 |

Number of pages | 6 |

ISBN (Electronic) | 0818634421, 9780818634420 |

DOIs | |

State | Published - 1993 |

Externally published | Yes |

Event | 7th International Parallel Processing Symposium, IPPS 1993 - Newport, United States Duration: Apr 13 1993 → Apr 16 1993 |

### Publication series

Name | Proceedings of 7th International Parallel Processing Symposium, IPPS 1993 |
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### Conference

Conference | 7th International Parallel Processing Symposium, IPPS 1993 |
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Country/Territory | United States |

City | Newport |

Period | 4/13/93 → 4/16/93 |

### Bibliographical note

Funding Information:* a s work was supported by ISTEDIO through the Army Research Office grant U28408-MA-SDI and by the United States Army Research Office, Contract Number DAAL03-89-C-0038 at the University of Min- nesota Army High Performance Computing Research Center. 'nCUBEL2 is a registered trademark of nCUBE Corporation.

Publisher Copyright:

© 1993 IEEE.