Single-exception sorting networks and the computational complexity of optimal sorting network verification

In general, efficient non-blocking interconnection networks can be derived from sorting networks, and to this end, one may either follow the merge-based or the radix-based sorting paradigm. Both paradigms require special modifications to handle partial permutations. In this article, we present a general lemma about half cleaner modules that were introduced as building blocks in Batcher’s bitonic sorting network. This lemma is the key to prove the correctness of many known optimizations of interconnection networks. In particular, we first show how to use any ternary sorter and a half cleaner for implementing an efficient split module as required for radix-based sorting networks for partial permutations. Second, our lemma formally proves the correctness of another known optimization of the Batcher-Banyan network.

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Using Sorting Networks for Skill Building and Reasoning

Mathematics Teaching in the Middle School ◽

10.5951/mtms.12.6.0308 ◽

2007 ◽

Vol 12 (6) ◽

pp. 308-311

Author(s):

Robert Andre ◽

Lynda R. Wiest

Keyword(s):

Middle School ◽

Middle School Students ◽

School Students ◽

Sorting Network ◽

Sorting Networks ◽

Pencil And Paper ◽

Skill Building

“When are we going to do that tarp thing again?” Andre's middle school students often ask. “When you can tell me what it is properly called,” is his response. “We should practice our math on the sorting network,” the students recall. This is a regular request that author Robert Andre often honors because he has found that his students truly enjoy the opportunity to walk about the classroom practicing skills and mental math rather than sit in their chairs working with pencil and paper.

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On the usage of sorting networks to control greenhouse climatic factors

International Journal of Distributed Sensor Networks ◽

10.1177/1550147718756871 ◽

2018 ◽

Vol 14 (2) ◽

pp. 155014771875687 ◽

Cited By ~ 1

Author(s):

Blanca C López Ramírez ◽

Giovanni Guzmán ◽

Wadee Alhalabi ◽

Nareli Cruz-Cortés ◽

Miguel Torres-Ruiz ◽

...

Keyword(s):

Control System ◽

State Of The Art ◽

Climatic Factors ◽

Small Data ◽

Climate Control ◽

Sorting Network ◽

Sorting Networks ◽

Adaptive Classification ◽

Input Size

The goal of this article is the application of a non-adaptive classification algorithm to support the variable management process for internal climate control. The protected agriculture has given many advantages for the care and improvement in the production of almost any food. This work is focused on improving a control system for climate variables. The decision for activating an actuator for the correct care of the crop is very important. A sorting network technique with predefined compare–interchange operations and designed to order data very efficiently is proposed. This approach has been applied to the process of handling actuators within a control system. An advantage of using the sorting networks is that it has an inflexibility when processing a data list; it always takes the same units of time and is executed in the same number of operations for an input size of n. Sorting network–based applications are scarce in the state-of-the-art because there are not many techniques that are effective for sorting very small data sizes. The use of sorting networks in the process of assessing the determination of actuators is proposed. This operation is scheduled in the design of control and performed at each reading back data.

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A Sorting Network on Trees

Parallel Processing Letters ◽

10.1142/s0129626419500154 ◽

2019 ◽

Vol 29 (04) ◽

pp. 1950015

Author(s):

Avah Banerjee ◽

Dana Richards

Keyword(s):

Complete Graph ◽

Maximum Degree ◽

Graph Topology ◽

Sorting Network ◽

Sorting Networks ◽

Underlying Graph ◽

Sorting Algorithms ◽

Oblivious Sorting

Sorting networks are a class of parallel oblivious sorting algorithms. Not only do they have interesting theoretical properties but they can be fabricated. A sorting network is a sequence of parallel compare-exchange operations using comparators which are grouped into stages. This underlying graph defines the topology of the network. The majority of results on sorting networks concern the unrestricted case where the underlying graph is the complete graph. Prior results are also known for paths, hypercubes, and meshes. In this paper we introduce a sorting network whose underlying topology is a tree and formalize the concept of sorting networks on a restricted graph topology by introducing a new parameter for graphs called its sorting number. The main result of the paper is a description of an [Formula: see text] depth sorting network on a tree with maximum degree [Formula: see text].

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AN 11-STEP SORTING NETWORK FOR 18 ELEMENTS

Parallel Processing Letters ◽

10.1142/s0129626409000092 ◽

2009 ◽

Vol 19 (01) ◽

pp. 97-103 ◽

Cited By ~ 2

Author(s):

SHERENAZ W. AL-HAJ BADDAR ◽

KENNETH E. BATCHER

Keyword(s):

Interconnection Networks ◽

Cost Effective ◽

Multistage Interconnection Networks ◽

Sorting Network ◽

Sorting Networks ◽

12 Steps

Sorting networks are cost-effective multistage interconnection networks with sorting capabilities. These networks theoretically consume Θ( NlogN ) comparisons. However, the fastest implementable sorting networks built so far consume Θ( Nlog 2 N ) comparisons, and generally, use the Merge-sorting strategy to sort the input. An 18-element network using the Merge-sorting strategy needs at least 12 steps — here we show a network that sorts 18 elements in only 11 steps.

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Random Subnetworks of Random Sorting Networks

The Electronic Journal of Combinatorics ◽

10.37236/472 ◽

2010 ◽

Vol 17 (1) ◽

Author(s):

Omer Angel ◽

Alexander E. Holroyd

Keyword(s):

Cayley Graph ◽

Shortest Path ◽

Nearest Neighbor ◽

Great Circle ◽

Relative Order ◽

Expected Number ◽

Sorting Network ◽

Sorting Networks ◽

Particle Sorting ◽

Polya Urn

A sorting network is a shortest path from $12\cdots n$ to $n\cdots21$ in the Cayley graph of $S_n$ generated by nearest-neighbor swaps. For $m\leq n$, consider the random $m$-particle sorting network obtained by choosing an $n$-particle sorting network uniformly at random and then observing only the relative order of $m$ particles chosen uniformly at random. We prove that the expected number of swaps in location $j$ in the subnetwork does not depend on $n$, and we provide a formula for it. Our proof is probabilistic, and involves a Pólya urn with non-integer numbers of balls. From the case $m=4$ we obtain a proof of a conjecture of Warrington. Our result is consistent with a conjectural limiting law of the subnetwork as $n\to\infty$ implied by the great circle conjecture of Angel, Holroyd, Romik and Virág.

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