Efficient Parallel Dynamic Programming (1994)
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@MISC{Bradford94efficientparallel,
author = {Phillip G. Bradford},
title = {Efficient Parallel Dynamic Programming},
year = {1994}
}
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Abstract
In 1983, Valiant, Skyum, Berkowitz and Racko# showed that many problems with simple O#n 3 # sequential dynamic programming solutions are in the class NC. They used straight line programs to show that these problems can be solved in O#lg 2 n# time with n 9 processors. In 1988, Rytter used pebbling games to show that these same problems can be solved on a CREW PRAM in O#lg 2 n# time with n 6 =lg n processors. Recently, Huang, Liu and Viswanathan #23# and Galil and Park #15# give algorithms that improve this processor complexityby polylog factors. Using a graph structure that is analogous to the classical dynamic programming table, this paper improves these results. First, this graph characterization leads to a polylog time and n 6 =lg n processor algorithm that solves these problems. Second, there follows a subpolylog time and sublinear processor parallel approximation algorithm for the matrix chain ordering problem. Finally, this paper presents a n 3 =lg n processor and O...
