On optimal parallelization of sorting networks
نویسندگان
چکیده
منابع مشابه
Optimal Sorting Networks
This paper settles the optimality of sorting networks given in The Art of Computer Programming vol. 3 more than 40 years ago. The book lists efficient sorting networks with n ≤ 16 inputs. In this paper we give general combinatorial arguments showing that if a sorting network with a given depth exists then there exists one with a special form. We then construct propositional formulas whose satis...
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We solve a 40-year-old open problem on the depth optimality of sorting networks. In 1973, Donald E. Knuth detailed, in Volume 3 of “The Art of Computer Programming”, sorting networks of the smallest depth known at the time for n ≤ 16 inputs, quoting optimality for n ≤ 8. In 1989, Parberry proved the optimality of the networks with 9 ≤ n ≤ 10 inputs. In this article, we present a general techniq...
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متن کاملOptimal Metastability-Containing Sorting Networks
When setup/hold times of bistable elements are violated, they may become metastable, i.e., enter a transient state that is neither digital 0 nor 1 [13]. In general, metastability cannot be avoided, a problem that manifests whenever taking discrete measurements of analog values. Metastability of the output then reflects uncertainty as to whether a measurement should be rounded up or down to the ...
متن کاملThe Takeoff Towards Optimal Sorting Networks
A complete set of filters Fn for the optimal-depth n-input sorting network problem is such that if there exists an n-input sorting network of depth d then there exists one of the form C ⊕ C′ for some C ∈ Fn. Previous work on the topic presents a method for finding complete set of filters Rn,1 and Rn,2 that consists only of networks of depths one and two respectively, whose outputs are minimal a...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1990
ISSN: 0304-3975
DOI: 10.1016/0304-3975(90)90025-d