The distribution of cycles in breakpoint graphs of signed permutations

Breakpoint graphs are ubiquitous structures in the field of genome rearrangements. Their cycle decomposition has proved useful in computing and bounding many measures of (dis)similarity between genomes, and studying the distribution of those cycles is therefore critical to gaining insight on the distributions of the genomic distances that rely on it. We extend here the work initiated by Doignon and Labarre, who enumerated unsigned permutations whose breakpoint graph contains $k$ cycles, to signed permutations, and prove explicit formulas for computing the expected value and the variance of the corresponding distributions, both in the unsigned case and in the signed case. We also compare these distributions to those of several well-studied distances, emphasising the cases where approximations obtained in this way stand out. Finally, we show how our results can be used to derive simpler proofs of other previously known results

Théophane et l'octroi de la liberté à Mytilène: Question de methode

No Abstract

Sorting by Prefix Block-Interchanges

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 using as few such operations as possible. We give a 2-approximation algorithm for this problem, show how to obtain improved lower and upper bounds on the corresponding distance, and determine the largest possible value for that distance

Increasing international footprint of a natural stone business

DPS tones is a Portuguese medium-sized company that works in the Cutting, Shaping and Finishing Stone business. This company has already a significant international footprint, dealing mainly with direct exports. Facing a saturated domestic market, DP aims to extend its’ lifecycle and find out new ways to gain competitive advantages. Accordingly, this project will analyse the current and future state of the CSF industry and assess possible target markets for DP to expand to. Afterwards, an entry strategy and marketing plan will be developed as well as a financial plan to evaluate the viability of the project proposed

Shannon Cain, ed., Roadside Curiosities. Stories about American Pop Culture

Roadside Curiosities is a collection of contemporary short stories which promises to marry “highbrow” and “lowbrow,” “literary fiction to American popular culture” (back cover). This union takes the form of twenty short stories selected by Shannon Cain, herself a short-story writer as well as a creative writing teacher, featuring Madonna, a superhero, the spectral image of Cary Grant, the hero of the Donkey Kong video game and more. In her introduction to the collection, Cain surprisingly re..

Lower bounding edit distances between permutations

International audienceA number of fields, including the study of genome rearrangements and the design of interconnection networks, deal with the connected problems of sorting permutations in "as few moves as possible", using a given set of allowed operations, or computing the number of moves the sorting process requires, often referred to as the distance of the permutation. These operations often act on just one or two segments of the permutation, e.g. by reversing one segment or exchanging two segments. The cycle graph of the permutation to sort is a fundamental tool in the theory of genome rearrangements, and has proved useful in settling the complexity of many variants of the above problems. In this paper, we present an algebraic reinterpretation of the cycle graph of a permutation π as an even permutation π, and show how to reformulate our sorting problems in terms of particular factorisations of the latter permutation. Using our framework, we recover known results in a simple and unified way, and obtain a new lower bound on the prefix transposition distance (where a prefix transposition displaces the initial segment of a permutation), which is shown to outperform previous results. Moreover, we use our approach to improve the best known lower bound on the prefix transposition diameter from 2n/3 to ⌊3n/4⌋, and investigate a few relations between some statistics on π and π

Théophane et l'octroi de la liberté à Mytilène: Question de methode

No Abstract

Decomposing Cubic Graphs into Connected Subgraphs of Size Three

Let $S=\{K_{1,3},K_3,P_4\}$ be the set of connected graphs of size 3. We study the problem of partitioning the edge set of a graph $G$ into graphs taken from any non-empty $S'\subseteq S$. The problem is known to be NP-complete for any possible choice of $S'$ in general graphs. In this paper, we assume that the input graph is cubic, and study the computational complexity of the problem of partitioning its edge set for any choice of $S'$. We identify all polynomial and NP-complete problems in that setting, and give graph-theoretic characterisations of $S'$-decomposable cubic graphs in some cases.Comment: to appear in the proceedings of COCOON 201