New Bounds on Optimal Sorting Networks
Thorsten Ehlers,Mike Müller +1 more
- pp 167-176
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TLDR
It is shown that the new parallel sorting network for \(17\) inputs is optimal in the sense that no sorting network using less layers exists, and this solves the main open problem of Optimal sorting networks.Abstract:
We present new parallel sorting networks for \(17\) to \(20\) inputs. For \(17, 19,\) and \(20\) inputs these new networks are faster (i.e., they require fewer computation steps) than the previously known best networks. Therefore, we improve upon the known upper bounds for minimal depth sorting networks on \(17, 19,\) and \(20\) channels. Furthermore, we show that our sorting network for \(17\) inputs is optimal in the sense that no sorting network using less layers exists. This solves the main open problem of [D. Bundala & J. Zavodný. Optimal sorting networks, Proc. LATA 2014].read more
Citations
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Journal ArticleDOI
Sorting networks: to the end and back again
TL;DR: New properties of the front and back ends of sorting networks are studied, illustrating their utility when searching for bounds on optimal networks, and shed understanding on how sorting networks sort.
Journal ArticleDOI
Optimal-depth sorting networks
TL;DR: This work constructs SAT formulas whose unsatisfiability is sufficient for the existence of a depth-k sorting network, and uses an off-the-shelf SAT solver to prove optimality of the sorting networks listed by Knuth.
Posted Content
Even faster sorting of (not only) integers
TL;DR: In this paper, the fastest parallel sorter based on the radix algorithm is introduced, which is optimized to process huge amounts of data making use of modern multicore CPUs. But the main novelties include extremely optimized algorithm for handling tiny arrays (up to about a hundred of records) that could appear even billions times as subproblems to handle and improved processing of larger subarrays with better use of non-temporal memory stores.
Book ChapterDOI
Even Faster Sorting of (Not Only) Integers
TL;DR: RADULS2, the fastest parallel sorter based on radix algorithm, is introduced, optimized to process huge amounts of data making use of modern multicore CPUs.
Journal ArticleDOI
Engineering faster sorters for small sets of items
TL;DR: The results clearly show the potential of using conditional moves in the field of sorting algorithms, as when sorting only small sets of integers, the sorting networks outperform insertion sort.
References
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Proceedings ArticleDOI
Sorting networks and their applications
TL;DR: To achieve high throughput rates today's computers perform several operations simultaneously; not only are I/O operations performed concurrently with computing, but also, in multiprocessors, several computing operations are done concurrently.
Proceedings ArticleDOI
Probing-based preprocessing techniques for propositional satisfiability
Inês Lynce,Joao Marques-Silva +1 more
TL;DR: Puzzling-based preprocessing is proposed, an integrated approach for preprocessing propositional formulas that for the first time integrates in a single algorithm most of the existing formula manipulation techniques.
Book ChapterDOI
Optimal Sorting Networks
Daniel Bundala,Jakub Závodný +1 more
TL;DR: This paper gives general combinatorial arguments showing that if a sorting network with a given depth exists then there exists one with a special form, and constructs propositional formulas whose satisfiability is necessary for the existence of such a network.
Journal ArticleDOI
A computer-assisted optimal depth lower bound for nine-input sorting networks
TL;DR: It is demonstrated, using a combination of theoretical and experimental computer science, that there is no nine-input sorting network of depth six and there is an efficient algorithm for constructing and testing comparator networks of this form.