NDLI: The Dynamic Parallel Complexity of Computational Circuits

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Miller, Gary L. Teng, Shang-Hua
Copyright Year	1999
Abstract	We establish connections between parallel circuit evaluation and uniform algebraic closure properties of unary function classes. We use this connection in the development of time-efficient and processor-efficient parallel algorithms for the evaluation of algebraic circuits. Our algorithm provides a nontrivial upper bound on the parallel complexity of the circuit value problem over $\{{\Bbb R},\min,\max,+\}$ and $\{{\Bbb R}^{+},\min,\max,\times\}$. We partially answer an open question of Miller, Ramachandran, and Kaltofen by showing that circuits over a polynomial-bounded noncommutative semiring and circuits over infinite noncommutative semirings with a polynomial-bounded dimension over a commutative semiring can be evaluated in polylogarithmic time in their size and degree using a polynomial number of processors. We also present an improved parallel algorithm for Boolean circuits.
Starting Page	1664
Ending Page	1688
Page Count	25
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539795281724
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	5
Volume Number	28
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-28
Access Restriction	Subscribed
Subject Keyword	complexity parallel algorithms algebraic computations the circuit value problem Graphs and linear algebra Graph theory Boolean circuits NC problems
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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