Designing Sorting Networks: A New Paradigm
Springer Science & Business Media, Feb 2, 2012 - Computers - 136 pages
Designing Sorting Networks: A New Paradigm provides an in-depth guide to maximizing the efficiency of sorting networks, and uses 0/1 cases, partially ordered sets and Haase diagrams to closely analyze their behavior in an easy, intuitive manner.
This book also outlines new ideas and techniques for designing faster sorting networks using Sortnet, and illustrates how these techniques were used to design faster 12-key and 18-key sorting networks through a series of case studies.
Finally, it examines and explains the mysterious behavior exhibited by the fastest-known 9-step 16-key network. Designing Sorting Networks: A New Paradigm is intended for advanced-level students, researchers and practitioners as a reference book. Academics in the fields of computer science, engineering and mathematics will also find this book invaluable.
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2 Software Implementations
4 The 01Principle01Principle
5 A 16Key Sorting Network
6 The Sortnet Program
7 Divide and Conquer
8 Counting Strangers Strangers
11 The AKS Sorting Network
12 Ideas for Faster Networks
14 Sorting NetworksSorting Networks For Large N
15 Another Way of Handling StrangersStrangers
16 Thoughts on Minimizing StrangersStrangers
17 Case Studies
Appendix I Proofs of Theorems
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16 keys 22 keys Baddar and K. E. Bitonic Merging bitonic sequence BOOL BOOL(N bracket column corresponding keys ð Þ Designing Sorting Networks display distributive lattice e-halver ee ee ee eliminate example faster sorting networks finding a faster four steps GE(x Goodyear Aerospace H-sequence Haase diagram hexadecimal higher group input sizes integer Introduction to algorithms isotone K. E. Batcher key with label Knuth diagram lattice Lattice theory LE(x Leiserson max(A max(B merge sorting merge-sorting network min(A min(B minimize strangers N-key network N-key sorting network node number of 0/1-cases number of comparators number of keys number of steps number of strangers Ó Springer Science+Business OCTET ODD EVEN ODD ordered lists partial-orderings re-labeled reducing the number S. W. Al-Haj Baddar series of comparators Shmoo chart SHOW.STRNGR.CNTS shown in Fig shows single-segment poset sort N keys sorting algorithms Sortnet command Springer Science+Business Media steps to sort Theorem zeroes