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Lower Bounds on Correction Networks [chapter]

Grzegorz Stachowiak
2003 Lecture Notes in Computer Science  
The main application of such 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.  ... 
doi:10.1007/978-3-540-24587-2_24 fatcat:a7lnkelgqrag7mqgyfqusxnwka

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.  ... 

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]

J. Hromkovič, K. Loryś, P. Kanarek, R. Klasing, W. Unger, H. Wagener
1995 Lecture Notes in Computer Science  
A new 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.  ... 
doi:10.1007/3-540-59042-0_78 fatcat:d3wczqru3jbd5clotnsvi6fzxq

Fast periodic correction networks

Grzegorz Stachowiak
2006 Theoretical Computer Science  
To perform this task we construct a 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.  ... 
doi:10.1016/j.tcs.2005.11.031 fatcat:q7zxj2tswjdajhaiwhpmhjiu6y

A Superlogarithmic Lower Bound for Shuffle-Unshuffle Sorting Networks

C. G. Plaxton
2000 Theory of Computing Systems  
Recently, n-input shuffleunshuffle 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] .  ... 
doi:10.1007/s002240010001 fatcat:pn4rzqk4rvhk3lnj5saxq34rrm

A randomized, o(log w)-depth 2 smoothing network

Marios Mavronicolas, Thomas Sauerwald
2009 Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures - SPAA '09  
to bound the 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  ... 
doi:10.1145/1583991.1584043 dblp:conf/spaa/MavronicolasS09 fatcat:b4fqutwzircizeyex74cthahdm

A combinatorial treatment of balancing networks

Costas Busch, Marios Mavronicolas
1996 Journal of the ACM  
and 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] .  ... 
doi:10.1145/234752.234754 fatcat:burrvtnk4vc6zhbrpjtpbai7qi

A combinatorial treatment of balancing networks

Costas Busch, Marios Mavronicolas
1994 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing - PODC '94  
and 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] .  ... 
doi:10.1145/197917.198092 dblp:conf/podc/BuschM94 fatcat:j6tfolhwk5d2tdd7lwdak66zni

EMD-RBFNN Coupling Prediction Model of Complex Regional Groundwater Depth Series: A Case Study of the Jiansanjiang Administration of Heilongjiang Land Reclamation in China

Qiang Fu, Dong Liu, Tianxiao Li, Song Cui, Yuxiang Hu
2016 Water  
groundwater 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.  ... 
doi:10.3390/w8080340 fatcat:5hkfvc4xurcdthkwojcacz2dh4

Faster 3-Periodic Merging Networks [article]

Marek Piotrów
2014 arXiv   pre-print
The challenging task is to construct such 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.  ... 
arXiv:1401.0396v1 fatcat:unw7x4mucfewtnf6cca4wfnq3i

Periodification scheme: constructing sorting networks with constant period

Mirosław kutyłowski, Krzysztof Loryś, Brigitte Oesterdiekhoff, Rolf Wanka
2000 Journal of the ACM  
We are interested in comparator 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.  ... 
doi:10.1145/355483.355490 fatcat:yp4pxesxgzgxrlholmltsd63ya

An Elegant Algorithm for the Construction of Suffix Arrays [article]

Sanguthevar Rajasekaran, Marius Nicolae
2013 arXiv   pre-print
The suffix array consists of the 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.  ... 
arXiv:1307.1417v1 fatcat:ippvb2jj6fbfbgjmm7mpumilqm
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