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Lower Bounds on Correction Networks
[chapter]

2003
*
Lecture Notes in Computer Science
*

The main application of such

doi:10.1007/978-3-540-24587-2_24
fatcat:a7lnkelgqrag7mqgyfqusxnwka
*networks*is producing fault-tolerant*sorting**networks*. We show the lower bound 1.44 log 2 N on the*depth*of correction*networks*settling an open problem from [7] . ... Correction*networks*are comparator*networks*that*sort*inputs differing from*sorted*sequences of length N in a small number of positions. ... Assume we have a large*sorted*database with N entries. In some*period*of time we make t modifications of the database and want to have it*sorted*back by a comparator*network*. ...##
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Page 6802 of Mathematical Reviews Vol. , Issue 2002I
[page]

2002
*
Mathematical Reviews
*

*networks*with

*constant*

*period*. ... Known

*periodic*balanced

*sorting*

*networks*of

*period*logn, latency log’n, and cost (mlog’n)/2 lead to an (nlogn)/2-cost circuit that can

*sort*in the same asymptotic time as the full

*network*when used logn ...

##
###
Page 7318 of Mathematical Reviews Vol. , Issue 90M
[page]

1990
*
Mathematical Reviews
*

The AKS-

*sorting**network*(Ajtai, Komlés, Szemerédi) with*depth*@(logn) is, because of the very large*constant*factor, only a theoretical solution. ... Batcher’s odd-even*sorting**network*with*depth*@(log” n) is more efficient in practice. Batcher’s*network*is based on a 2-way merge. ...##
###
Page 2752 of Mathematical Reviews Vol. , Issue 99d
[page]

1991
*
Mathematical Reviews
*

General methods are given for constructing a comparator

*network*and a hypercubic comparator*network*of logarithmic*depth*which*sort*a vast majority of permutations, and a hy- percubic*sorting**network*of ... Summary: “We consider the problem of merging two*sorted*sequences on*constant*degree*networks*performing compare- exchange operations only. ...##
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Page 5539 of Mathematical Reviews Vol. , Issue 95i
[page]

1995
*
Mathematical Reviews
*

“Odd-even transposition

*sort*gives a*periodic**sorting**network*of*depth*2 that*sorts*m numbers in n/2 iterations. ... Summary: “Comparator*networks*of*constant**depth*can be used for*sorting*in the following way. ...##
###
On the sizes of permutation networks and consequences for efficient simulation of hypercube algorithms on bounded-degree networks
[chapter]

1995
*
Lecture Notes in Computer Science
*

A new

doi:10.1007/3-540-59042-0_78
fatcat:d3wczqru3jbd5clotnsvi6fzxq
*sorting**network*as well as an essential improvement of gossiping in vertex-disjoint path mode in bounded-degree*networks*follow. ... A consequence of our results is a construction of a 4-degree*network*which can simulate each communication step of any hypercube algorithm using edges from at most a*constant*number of di erent dimensions ... This*network*has*depth*8 log log N and the*sorting*algorithm*periodically*uses the*network*O(log N (log log N) 2 ) times. ...##
###
Fast periodic correction networks

2006
*
Theoretical Computer Science
*

To perform this task we construct a

doi:10.1016/j.tcs.2005.11.031
fatcat:q7zxj2tswjdajhaiwhpmhjiu6y
*constant**depth*comparator*network*that is applied*periodically*. ... We consider the problem of*sorting*N-element inputs differing from already*sorted*sequences by t small changes. ... If t is about the same as N, then the periodification scheme gives a practical*periodic**sorting**network*of*depth*3 requiring O(log 3 N) = O(log 3 t) iterations. ...##
###
A Superlogarithmic Lower Bound for Shuffle-Unshuffle Sorting Networks

2000
*
Theory of Computing Systems
*

Recently, n-input shuffleunshuffle

doi:10.1007/s002240010001
fatcat:pn4rzqk4rvhk3lnj5saxq34rrm
*sorting**networks*with*depth*2 O( p lg lg n) lg n have been discovered. ...*sorting**network*. ... A*periodic**sorting**network*of*depth*O(lg n) and running time O(lg 2 n) was given by Dowd, Perl, Rudolph, and Saks [9] . ...##
###
A randomized, o(log w)-depth 2 smoothing network

2009
*
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures - SPAA '09
*

to bound the

doi:10.1145/1583991.1584043
dblp:conf/spaa/MavronicolasS09
fatcat:b4fqutwzircizeyex74cthahdm
*depth*complexity of*sorting*by a small*constant*times the*depth*complexity of smoothing, or to construct a small-*depth*smoothing*network*that makes no use of*sorting**networks*. " In this work ... use of the famous AKS*sorting**network*due to Ajtai, Komlós and Szemerédi [3] (with*depth*Θ(lg w)) as a building block in the construction due to its huge*constants*hidden in the Θ(lg w) notation. (4) It ... lg w)-*depth**sorting**network*improving on the AKS*sorting**network*(in terms of the hidden*constants*) is to bound the*depth*complexity of*sorting*by a small*constant*times the*depth*complexity of 2-smoothing ...##
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A combinatorial treatment of balancing networks

1996
*
Journal of the ACM
*

and

doi:10.1145/234752.234754
fatcat:burrvtnk4vc6zhbrpjtpbai7qi
*sorting**networks*. ... We propose these combinatorial conditions to be \balancing analogs" of the well known Zero-One principle holding for*sorting**networks*. ...*Periodic**sorting**networks*of*constant**period*are easy to implement in VLSI technology [16] . ...##
###
A combinatorial treatment of balancing networks

1994
*
Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing - PODC '94
*

and

doi:10.1145/197917.198092
dblp:conf/podc/BuschM94
fatcat:j6tfolhwk5d2tdd7lwdak66zni
*sorting**networks*. ... We propose these combinatorial conditions to be \balancing analogs" of the well known Zero-One principle holding for*sorting**networks*. ...*Periodic**sorting**networks*of*constant**period*are easy to implement in VLSI technology [16] . ...##
###
EMD-RBFNN Coupling Prediction Model of Complex Regional Groundwater Depth Series: A Case Study of the Jiansanjiang Administration of Heilongjiang Land Reclamation in China

2016
*
Water
*

groundwater

doi:10.3390/w8080340
fatcat:5hkfvc4xurcdthkwojcacz2dh4
*depth*has a significant one-year*periodic*character and an increasing trend. ... (EMD) and a radial basis function neural*network*(RBFNN). ... Determine the*Network*Training Parameters Set the RBFNN target error GOAL = 0.0001, spread*constant*SPREAD = 1, and number of maximum neurons MN = 40. ...##
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Faster 3-Periodic Merging Networks
[article]

2014
*
arXiv
*
pre-print

The challenging task is to construct such

arXiv:1401.0396v1
fatcat:unw7x4mucfewtnf6cca4wfnq3i
*networks*of small*depth*. The first constructions of merging*networks*with a*constant**period*were given by Kutyłowski, Loryś and Oesterdikhoff. ... They have given 3-*periodic**network*that merges two*sorted*sequences of N numbers in time 12 N and a similar*network*of*period*4 that works in 5.67 N. ... (2) For each k ≥ 1, CW k is a k-pass*periodic**sorting**network*. We would like to implement a version of this*network*as a*constant*-*periodic*comparator*network*. ...##
###
Periodification scheme: constructing sorting networks with constant period

2000
*
Journal of the ACM
*

We are interested in comparator

doi:10.1145/355483.355490
fatcat:yp4pxesxgzgxrlholmltsd63ya
*networks*of a*constant**period*, due to their potential applications in hardware design. Previously, very little was known on such*networks*. ... We consider comparator*networks*M that are used repeatedly: while the output produced by M is not*sorted*, it is fed again into M.*Sorting*algorithms working in this way are called*periodic*. ... We are grateful to Friedhelm Meyer auf der Heide for presenting us the problem of*periodic**sorting*with*constant**depth**networks*. ...##
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An Elegant Algorithm for the Construction of Suffix Arrays
[article]

2013
*
arXiv
*
pre-print

The suffix array consists of the

arXiv:1307.1417v1
fatcat:ippvb2jj6fbfbgjmm7mpumilqm
*sorted*suffixes of a string. There are several linear time suffix array construction algorithms (SACAs) known in the literature. ...*Periods*of any length are eventually detected because the*depth*of*sorting*in each bucket increases after each*sort*operation. ... Underlines show the*depth*of*sorting*in a bucket at a given time. The initial radix*sort*has*depth*1 for illustration purpose. ...
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