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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…

Discrete Mathematics · Computer Science 2025-03-12 Lapo Cioni , Luca Ferrari , Rebecca Smith

Given two strings $T$ and $S$ and a set of strings $P$, for each string $p \in P$, consider the unique substrings of $T$ that have $p$ as their prefix and $S$ as their suffix. Two problems then come to mind; the first problem being the…

Data Structures and Algorithms · Computer Science 2022-04-19 Laurentius Leonard , Ken Tanaka

Generalizing stack sorting and $c$-sorting for permutations, we define the permutree sorting algorithm. Given two disjoint subsets $U$ and $D$ of $\{2, \dots, n-1\}$, the $(U,D)$-permutree sorting tries to sort the permutation $\pi \in…

Combinatorics · Mathematics 2023-07-13 Vincent Pilaud , Viviane Pons , Daniel Tamayo Jiménez

In this paper we study several variations of the \emph{pancake flipping problem}, which is also well known as the problem of \emph{sorting by prefix reversals}. We consider the variations in the sorting process by adding with prefix…

Data Structures and Algorithms · Computer Science 2009-05-04 Masud Hasan , Atif Rahman , M. Sohel Rahman , Mahfuza Sharmin , Rukhsana Yeasmin

Pancake flipping, a famous open problem in computer science, can be formalised as the problem of sorting a permutation of positive integers using as few prefix reversals as possible. In that context, a prefix reversal of length k reverses…

Data Structures and Algorithms · Computer Science 2011-02-07 Anthony Labarre , Josef Cibulka

A polynomial algorithm is obtained for the NP-complete linear ordering problem.

Computational Complexity · Computer Science 2007-05-23 Givi Bolotashvili

We address the problem of finding the minimum decomposition of a permutation in terms of transpositions with non-uniform cost. For arbitrary non-negative cost functions, we describe polynomial-time, constant-approximation decomposition…

Information Theory · Computer Science 2010-07-27 Farzad Farnoud , Olgica Milenkovic

In this work, we consider a restricted case of the well studied Sorting by Block Interchanges problem. We put an upper bound k on the length of the blocks (substrings) to be interchanged at each step. We call the problem Sorting by k-Block…

Computational Complexity · Computer Science 2011-10-06 Swapnoneel Roy

We initiate the study of sorting permutations using prefix block-interchanges, which exchange any prefix of a permutation with another non-intersecting interval. The goal is to transform a given permutation into the identity permutation…

Data Structures and Algorithms · Computer Science 2022-08-29 Anthony Labarre

In this article, we study the problem of finding the longest common separable pattern between several permutations. We give a polynomial-time algorithm when the number of input permutations is fixed and show that the problem is NP-hard for…

Combinatorics · Mathematics 2007-06-13 Mathilde Bouvel , Dominique Rossin , Stephane Vialette

We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…

Discrete Mathematics · Computer Science 2021-01-19 Dariusz Dereniowski , Wieslaw Kubiak

We show that the left-greedy algorithm is a better algorithm than the right-greedy algorithm for sorting permutations using t stacks in series when t>1. We also supply a method for constructing some permutations that can be sorted by t…

Combinatorics · Mathematics 2007-05-23 Rebecca Smith

Sorting a permutation by reversals is a famous problem in genome rearrangements. Since 1997, quite some biological evidence were found that in many genomes the reversed regions are usually flanked by a pair of inverted repeats. This type of…

Data Structures and Algorithms · Computer Science 2023-02-09 Xin Tong , Yixiao Yu , Ziyi Fang , Haitao Jiang , Lusheng Wang , Binhai Zhu , Daming Zhu

The topic of the article is the parametric study of the complexity of algorithms on arrays of pairwise distinct integers. We introduce a model that takes into account the non-uniformness of data, which we call the Ewens-like distribution of…

Discrete Mathematics · Computer Science 2016-05-11 Nicolas Auger , Mathilde Bouvel , Cyril Nicaud , Carine Pivoteau

We study a sorting machine consisting of two stacks in series where the first stack has the added restriction such that entries in the stack must be in decreasing order from top to bottom. We give the basis of the class of permutations that…

Combinatorics · Mathematics 2013-01-30 Rebecca Smith

A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NP-hard. Here we show…

Combinatorics · Mathematics 2009-05-18 Mathilde Bouvel , Cedric Chauve , Marni Mishna , Dominique Rossin

Sorting and hashing are two completely different concepts in computer science, and appear mutually exclusive to one another. Hashing is a search method using the data as a key to map to the location within memory, and is used for rapid…

Data Structures and Algorithms · Computer Science 2007-05-23 William F. Gilreath

We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations…

Combinatorics · Mathematics 2012-03-13 Anders Claesson , Henning Úlfarsson

Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…

Data Structures and Algorithms · Computer Science 2019-08-14 Benjamin Aram Berendsohn , László Kozma , Dániel Marx

We prove that computing an evolutionary ordering of a family of sets, i.e. an ordering where each set intersects with --but is not included in-- the union earlier sets, is NP-hard.

Computational Complexity · Computer Science 2014-10-27 Laurent Bulteau , Gustavo Sacomoto , Blerina Sinaimeri