Designing Sorting Networks: A New Paradigm by Sherenaz W. Al-Haj Baddar

By Sherenaz W. Al-Haj Baddar

Designing Sorting Networks: a brand new Paradigm presents an in-depth consultant to maximizing the potency of sorting networks, and makes use of 0/1 instances, in part ordered units and Haase diagrams to heavily learn their habit in a simple, intuitive demeanour.

This e-book additionally outlines new principles and methods for designing speedier sorting networks utilizing Sortnet, and illustrates how those strategies have been used to layout speedier 12-key and 18-key sorting networks via a sequence of case reviews.

Finally, it examines and explains the mysterious habit exhibited by way of the fastest-known 9-step 16-key community. Designing Sorting Networks: a brand new Paradigm is meant for advanced-level scholars, researchers and practitioners as a reference publication. lecturers within the fields of desktop technology, engineering and arithmetic also will locate this publication invaluable.

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Additional resources for Designing Sorting Networks: A New Paradigm

Example text

An 11-step 18-key network and a 12-step 22-key network were discovered using Sortnet as described in [3]. These two networks are each one step faster than the corresponding mergesorting networks. This discovery helped find two faster networks for N = 17 and for N = 21 as well. The reader may refer to Chap. 17 for more details. References 1. Cormen T, Leiserson C, Rivest R, Stein C (2001) Introduction to algorithms, 2nd edn. McGraw-Hill Book Company, USA 2. Brassard G, Bratley P (1996) Fundamentals of algorithmics.

If x B y and y B x, then x = y. • If x B y and y B z, then x B z. 1 Isotone Functions Given two posets, X and Y, we say that f is a function from X to Y if for every x in X, f(x) is in Y. If X contains |X| elements and Y contains |Y| elements then there are |Y||X| different functions from X to Y [1]. As examples, Let P and Q be the posets diagramed in Figs. 2, respectively. Then there are 32 = 9 different functions from P to Q as shown in Fig. 3 and 3 2 = 8 different functions from Q to P as shown in Fig.

Doubling the size of a merge network adds another level of comparators to it. This will add another step to the whole sorting network unless the comparators in 46 7 Divide and Conquer Fig. 3 Straddling the Boundaries of the Sorted Groups Fig. 4 Expanding the Straddling with Merge Networks the merge network can use the same steps as the final steps in the group-sorting networks. If we examine the sorting network in Figs. 49 and 51 of [1] we notice that every one of them sorts a number of their lowest keys and highest keys before sorting their keys in the center.

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