论文信息 - A Sublinear Parallel Algorithm for Some Dynamic Programming Problems

A Sublinear Parallel Algorithm for Some Dynamic Programming Problems

Abstract This paper presents a sublinear parallel algorithm for dynamic programming problems such as computing an optimal order of matrix multiplications, an optimal binary search tree or an optimal triangulation of polygons. An algorithm was presented in Rytter (1988) which runs in O(log 2 n ) time using O( n 6 /log n ) processors. An algorithm is presented in this paper which runs in O(√ n log n ) time using O( n 3.5 /log n ) processors on a CREW PRAM. Amongst known sublinear algorithms, this is an improvement by a factor of O( n 2 log n ) in terms of processor-time product.

[1] Jeffrey D. Smith,et al. Design and Analysis of Algorithms , 2009, Lecture Notes in Computer Science.

[2] Jeffrey Scott Vitter,et al. New Classes for Parallel Complexity: A Study of Unification and Other Complete Problems for P , 1986, IEEE Transactions on Computers.

[3] Wojciech Rytter,et al. On Efficient Parallel Computations for some Dynamic Programming Problems , 1988, Theor. Comput. Sci..

[4] Wojciech Rytter,et al. The Complexity of Two-Way Pushdown Automata and Recursive Programs , 1985 .

[5] Mikhail J. Atallah,et al. Constructing trees in parallel , 1989, SPAA '89.

[6] Benjamin W. Wah,et al. Systolic processing for dynamic programming problems , 1988, ICPP.

[7] H. T. Kung,et al. Direct VLSI Implementation of Combinatorial Algorithms , 1979 .

[8] Wojciech Rytter,et al. Efficient parallel algorithms , 1988 .