Parallel Restructuring and Evaluation of Expressions

Abstract In this paper we describe a boolean network of size O ( N 2 log N ) which accepts a fully parenthesized N -variable expression over a given semiring and produces its value in O (log N ) time. The network consists of two components: a preprocessor and a universal evaluator. The preprocessor computes the destinations of the expression terms and routes them to the correct input terminals of the universal evaluator.

[1]  David E. Muller,et al.  Restructuring of Arithmetic Expressions For Parallel Evaluation , 1976, JACM.

[2]  Uzi Vishkin,et al.  Optimal parallel generation of a computation tree form , 1985, TOPL.

[3]  David J. Kuck,et al.  Time Bounds on the Parallel Evaluation of Arithmetic Expressions , 1975, SIAM J. Comput..

[4]  Kiyoshi Maruyama,et al.  The Parallel Evaluation of Arithmetic Expressions Without Division , 1973, IEEE Transactions on Computers.

[5]  Arthur L. Delcher,et al.  Optimal Parallel Evaluation of Tree-Structured Computations by Raking , 1988, AWOC.

[6]  Gary L. Miller,et al.  Parallel tree contraction and its application , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[7]  Richard Cole,et al.  Optimal Parallel Algorithms for Expression Tree Evaluation and List Ranking , 1988, AWOC.

[8]  S. N. Maheshwari,et al.  Efficient VLSI Networks for Parallel Processing Based on Orthogonal Trees , 1983, IEEE Transactions on Computers.

[9]  David E. Muller,et al.  Efficient Parallel Evaluation of Boolean Expressions , 1976, IEEE Transactions on Computers.

[10]  David E. Muller,et al.  Bounds to Complexities of Networks for Sorting and for Switching , 1975, JACM.

[11]  Wojciech Rytter,et al.  An Optimal Parallel Algorithm for Dynamic Expression Evaluation and Its Applications , 1986, FSTTCS.

[12]  Samuel R. Buss,et al.  An Optimal Parallel Algorithm for Formula Evaluation , 1992, SIAM J. Comput..

[13]  Richard P. Brent,et al.  The Parallel Evaluation of General Arithmetic Expressions , 1974, JACM.

[14]  Kiyoshi M. Maruyama,et al.  On the Parallel Evaluation of Polynomials , 1973, IEEE Transactions on Computers.

[15]  S. Rao Kosaraju,et al.  A tree-partitioning technique with applications to expression evaluation and term matching , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[16]  Jean-Loup Baer,et al.  Compilation of arithmetic expressions for parallel computations , 1968, IFIP Congress.

[17]  Joachim von zur Gathen,et al.  Parallel Arithmetic Computations: A Survey , 1986, MFCS.