A highly parallel algorithm for multistage optimization problems and shortest path problems
John K. Antonio, Wei K. Tsai, Garng Morton Huang
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.
Journal of Parallel and Distributed Computing
https://doi.org/10.1016/0743-7315(91)90126-T
Shortest Path Problem
Optimization Problem
Time Complexity
Convolutional Codes
Parallel Computers
Divides
Antonio, J. K., Tsai, W. K., & Huang, G. M. (1991). A highly parallel algorithm for multistage optimization problems and shortest path problems. 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.
In: Journal of Parallel and Distributed Computing, Vol. 12, No. 3, 01.01.1991, p. 213-222.
Antonio, JK, Tsai, WK & Huang, GM 1991, 'A highly parallel algorithm for multistage optimization problems and shortest path problems', Journal of Parallel and Distributed Computing, vol. 12, no. 3, pp. 213-222. https://doi.org/10.1016/0743-7315(91)90126-T
Antonio JK, Tsai WK, Huang GM. A highly parallel algorithm for multistage optimization problems and shortest path problems. Journal of Parallel and Distributed Computing. 1991 Jan 1;12(3):213-222. https://doi.org/10.1016/0743-7315(91)90126-T
Antonio, John K. ; Tsai, Wei K. ; Huang, Garng Morton. / A highly parallel algorithm for multistage optimization problems and shortest path problems. In: Journal of Parallel and Distributed Computing. 1991 ; Vol. 12, No. 3. pp. 213-222.
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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.",
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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.
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