Computing the cycles in the perfect shuffle permutation

Ellis, John; Krahn, Tobias; Fan, Hongbing

doi:10.1016/s0020-0190(00)00103-4

Cited by 12 publications

(6 citation statements)

References 8 publications

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“…These permutations have many applications (e.g., parallel processing [30], Fast Fourier Transforms (FFT) [30,11], Kronecker products [12,11], encryption [31], sorting [30], and merging [14,10,17]). Ellis et al [16,15] use a number-theoretic approach to compute representative elements of the disjoint cycles of the perfect shuffle and the k-way perfect shuffle, thus making a sequential in-place approach possible. Jain [21] relies on the fact that 2 is primitive root of 3 k for any k ≥ 1, which makes it possible to compute the representative elements of the disjoint cycles recursively for any N .…”

Section: Previous Work On Permutationsmentioning

confidence: 99%

Beyond Binary Search: Parallel In-Place Construction of Implicit Search Tree Layouts

Berney

Casanova

Karsin

et al. 2022

IEEE Trans. Comput.

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Section: Previous Work On Permutationsmentioning

confidence: 99%

Beyond Binary Search: Parallel In-Place Construction of Implicit Search Tree Layouts

Berney

Casanova

Karsin

et al. 2022

IEEE Trans. Comput.

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“…La factorisation du k-perfect shuffle est un problème résolu dans Ellis et al (2002). La méthode est basée sur le constat suivant.…”

Section: Diagonalisation Alternée Des Dépliages Intérêt Des Shufflesunclassified

“…On peut montrer que réciproquement, pour tout d|m, toute classe d'un élément de (Z/dZ) × selon k d multipliée par m/d est un cycle de σ k,n . Il reste alors à calculer ces classes, un algorithme pour ce faire est décrit dans Ellis et al (2002).…”

Section: Diagonalisation Alternée Des Dépliages Intérêt Des Shufflesunclassified

Hyperspectral Image Analysis

2020

Advances in Computer Vision and Pattern Recognition

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Total variation regularized non-negative matrix factorization for smooth hyperspectral unmixing 6 Autres problèmes rencontrés Algorithme 2 k-means++, voir Arthur et Vassilvitskii (2007) Entrée : (x i) i∈{1,••• ,m} les m éléments à partitionner {Nul besoin de centres initiaux.} Sortie : (c i) i∈{1,••• ,k} les k centres initiaux pour k-means (1) {Renvoie k centres permettant d'initialiser k-means.}

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“…Using hashing, one can also design an algorithm using expected O(n log n) time and O(log n) bits of space without any assumption on π (interestingly, a different application of randomisation is known to help in leader election in anonymous unidirectional rings [21]). Better cycle leaders algorithms are known for some specific permutations, such as the perfect shuffle [11].…”

Section: Introductionmentioning

confidence: 99%

Strictly In-Place Algorithms for Permuting and Inverting Permutations

Dudek¹,

Gawrychowski²,

Pokorski³

2021

Preprint

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We revisit the problem of permuting an array of length n according to a given permutation in place, that is, using only a small number of bits of extra storage. Fich, Munro and Poblete [FOCS 1990, SICOMP 1995 obtained an elegant O(n log n)-time algorithm using only O(log 2 n) bits of extra space for this basic problem by designing a procedure that scans the permutation and outputs exactly one element from each of its cycles. However, in the strict sense in place should be understood as using only an asymptotically optimal O(log n) bits of extra space, or storing a constant number of indices. The problem of permuting in this version is, in fact, a well-known interview question, with the expected solution being a quadratic-time algorithm. Surprisingly, no faster algorithm seems to be known in the literature.Our first contribution is a strictly in-place generalisation of the method of Fich et al. that works in Oε(n 1+ε ) time, for any ε > 0. Then, we build on this generalisation to obtain a strictly in-place algorithm for inverting a given permutation on n elements working in the same complexity. This is a significant improvement on a recent result of Guśpiel [arXiv 2019], who designed an O(n 1.5 )-time algorithm.

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Computing the cycles in the perfect shuffle permutation

Cited by 12 publications

References 8 publications

Beyond Binary Search: Parallel In-Place Construction of Implicit Search Tree Layouts

Beyond Binary Search: Parallel In-Place Construction of Implicit Search Tree Layouts

Hyperspectral Image Analysis

Strictly In-Place Algorithms for Permuting and Inverting Permutations

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