### Abstract

It appears that all of the known algorithms for solving multistage optimization problems are based explicitly on standard dynamic programming concepts. Such algorithms are inherently serial in the sense that computation must be completed at the current stage before meaningful computation can begin at the next stage. In this paper we present a technique which recursively divides the original problem into a set of smaller problems which can be solved in parallel. This technique is based on the recursive application of a simple aggregation procedure. For a multistage process with n stages, we show that our new algorithm can achieve a time complexity of O(log n). In contrast, competing algorithms based exclusively on the standard dynamic programming technique can only achieve a time complexity of Φ(n). The new algorithm is designed to operate on a tightly coupled parallel computer. As some important applications, it is shown that our algorithm can serve as a fast and efficient means of decoding convolutional codes, solving shortest path problems, and determining minimum-fuel flight paths.

Original language | English |
---|---|

Pages (from-to) | 213-222 |

Number of pages | 10 |

Journal | Journal of Parallel and Distributed Computing |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 1991 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Software
- Hardware and Architecture
- Computer Networks and Communications
- Artificial Intelligence

### Cite this

*Journal of Parallel and Distributed Computing*,

*12*(3), 213-222. https://doi.org/10.1016/0743-7315(91)90126-T

**A highly parallel algorithm for multistage optimization problems and shortest path problems.** / Antonio, John K.; Tsai, Wei K.; Huang, Garng Morton.

Research output: Contribution to journal › Article

*Journal of Parallel and Distributed Computing*, vol. 12, no. 3, pp. 213-222. https://doi.org/10.1016/0743-7315(91)90126-T

}

TY - JOUR

T1 - A highly parallel algorithm for multistage optimization problems and shortest path problems

AU - Antonio, John K.

AU - Tsai, Wei K.

AU - Huang, Garng Morton

PY - 1991/1/1

Y1 - 1991/1/1

N2 - It appears that all of the known algorithms for solving multistage optimization problems are based explicitly on standard dynamic programming concepts. Such algorithms are inherently serial in the sense that computation must be completed at the current stage before meaningful computation can begin at the next stage. In this paper we present a technique which recursively divides the original problem into a set of smaller problems which can be solved in parallel. This technique is based on the recursive application of a simple aggregation procedure. For a multistage process with n stages, we show that our new algorithm can achieve a time complexity of O(log n). In contrast, competing algorithms based exclusively on the standard dynamic programming technique can only achieve a time complexity of Φ(n). The new algorithm is designed to operate on a tightly coupled parallel computer. As some important applications, it is shown that our algorithm can serve as a fast and efficient means of decoding convolutional codes, solving shortest path problems, and determining minimum-fuel flight paths.

AB - It appears that all of the known algorithms for solving multistage optimization problems are based explicitly on standard dynamic programming concepts. Such algorithms are inherently serial in the sense that computation must be completed at the current stage before meaningful computation can begin at the next stage. In this paper we present a technique which recursively divides the original problem into a set of smaller problems which can be solved in parallel. This technique is based on the recursive application of a simple aggregation procedure. For a multistage process with n stages, we show that our new algorithm can achieve a time complexity of O(log n). In contrast, competing algorithms based exclusively on the standard dynamic programming technique can only achieve a time complexity of Φ(n). The new algorithm is designed to operate on a tightly coupled parallel computer. As some important applications, it is shown that our algorithm can serve as a fast and efficient means of decoding convolutional codes, solving shortest path problems, and determining minimum-fuel flight paths.

UR - http://www.scopus.com/inward/record.url?scp=0026186977&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026186977&partnerID=8YFLogxK

U2 - 10.1016/0743-7315(91)90126-T

DO - 10.1016/0743-7315(91)90126-T

M3 - Article

VL - 12

SP - 213

EP - 222

JO - Journal of Parallel and Distributed Computing

JF - Journal of Parallel and Distributed Computing

SN - 0743-7315

IS - 3

ER -