Related papers: Compressed Representations of Permutations, and Ap…
We introduce a new technique for the efficient management of large sequences of multidimensional data, which takes advantage of regularities that arise in real-world datasets and supports different types of aggregation queries. More…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
We introduce a new sorting device for permutations which makes use of a pop stack augmented with a bypass operation. This results in a sorting machine, which is more powerful than the usual Popstacksort algorithm and seems to have never…
Permutation is the different arrangements that can be made with a given number of things taking some or all of them at a time. The notation P(n,r) is used to denote the number of permutations of n things taken r at a time. Permutation is…
Given a real number beta>1, a permutation pi of length n is realized by the beta-shift if there is some x in [0,1] such that the relative order of the sequence x,f(x),...,f^{n-1}(x), where f(x) is the factional part of beta*x, is the same…
We describe and analyze different approaches to represent ordinal patterns. All of these can be found in the literature. The most important representations (plus sub-classes) are compared in terms of their applicability from different…
We consider the problem of learned transform compression where we learn both, the transform as well as the probability distribution over the discrete codes. We utilize a soft relaxation of the quantization operation to allow for…
Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of…
Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through…
We investigate dynamical properties of the set of permutations of $\mathbb{Z}^d$ with restricted movement, i.e., permutations $\pi $ of $\mathbb{Z}^d$ such that $\pi (\mathbf{n})-\mathbf{n}$ lies, for every $\mathbf{n}\in \mathbb{Z}^d$, in…
Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…
Can we do arithmetic in a completely different way, with a radically different data structure? Could this approach provide practical benefits, like operations on giant numbers while having an average performance similar to traditional…
The ubiquitous Variable-Byte encoding is one of the fastest compressed representation for integer sequences. However, its compression ratio is usually not competitive with other more sophisticated encoders, especially when the integers to…
In a system that performs both encryption and lossy compression, the conventional way is to compress first and then encrypt the compressed data. This separation approach proves to be optimal. In certain applications where sensitive…
In this paper a novel approach for matrix manipulation and indexing is proposed .Here the elements in a row of matrix are designated by numeric value called permutation index followed by the elements of the row being randomised. This is…
Let $m, n$ be positive integers such that $m>1$ divides $n$. In this paper, we introduce a special class of piecewise-affine permutations of the finite set $[1, n]:=\{1, \ldots, n\}$ with the property that the reduction $\pmod m$ of $m$…
The use of permutation polynomials has appeared, along to their compositional inverses, as a good choice in the implementation of cryptographic systems. Hence, there has been a demand for constructions of these polynomials which…
Given a string $S$ of $n$ integers in $[0,\sigma)$, a range minimum query RMQ$(i, j)$ asks for the index of the smallest integer in $S[i \dots j]$. It is well known that the problem can be solved with a succinct data structure of size $2n +…
We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations…
Lossy image compression is a many-to-one process, thus one bitstream corresponds to multiple possible original images, especially at low bit rates. However, this nature was seldom considered in previous studies on image compression, which…