Smoothsort's behavior on presorted sequences

In [5], Mehlhorn presented an algorithm for sorting nearly sorted sequences of length n in time 0(n(1+log(F/n))) where F is the number of initial inversions. More recently, Dijkstra[3] presented a new algorithm for sorting in situ. Without giving much evidence of it, he claims that his algorithm works well on nearly sorted sequences. In this note we show that smoothsort compares unfavorably to Mehlhorn's algorithm. We present a sequence of length n with O(nlogn) inversions which forces smoothsort to use time Omega(nlog n), contrasting to the time O(nloglogn) Mehlhorn's algorithm would need

Distributed Sorting

In this paper we present a distributed sorting algorithm, which is a variation on exchange sort, i.e., neighboring elements that are out of order are exchanged. We derive the algorithm by transforming a sequential algorithm into a distributed one. The transformation is guided by the distribution of the data over processes. First we discuss the case of two processes, and then the general case of one or more processes. Finally we propose a more efficient solution for the general case

ecoPrimers: inference of new DNA barcode markers from whole genome sequence analysis

Using non-conventional markers, DNA metabarcoding allows biodiversity assessment from complex substrates. In this article, we present ecoPrimers, a software for identifying new barcode markers and their associated PCR primers. ecoPrimers scans whole genomes to find such markers without a priori knowledge. ecoPrimers optimizes two quality indices measuring taxonomical range and discrimination to select the most efficient markers from a set of reference sequences, according to specific experimental constraints such as marker length or specifically targeted taxa. The key step of the algorithm is the identification of conserved regions among reference sequences for anchoring primers. We propose an efficient algorithm based on data mining, that allows the analysis of huge sets of sequences. We evaluate the efficiency of ecoPrimers by running it on three different sequence sets: mitochondrial, chloroplast and bacterial genomes. Identified barcode markers correspond either to barcode regions already in use for plants or animals, or to new potential barcodes. Results from empirical experiments carried out on a promising new barcode for analyzing vertebrate diversity fully agree with expectations based on bioinformatics analysis. These tests demonstrate the efficiency of ecoPrimers for inferring new barcodes fitting with diverse experimental contexts. ecoPrimers is available as an open source project at: http://www.grenoble.prabi.fr/trac/ecoPrimers

A forma matricial dos números de Leonardo

In this work we will investigate the generating matrices for the positive integers of the Leonardo sequence, as well as some inherent properties of these matrices. In order to perform the process of generalizing the matrix form of Leonardo’s numbers, the extension to the field of non-positive integers is performed, in which the study of these matrices is unpublished in this research. The matrix form relates the matrices to the Leonardo numbers, and by raising these matrices to nth power, we obtain some new relations of this sequence, thus knowing their respective terms.Neste trabalho serão investigadas as matrizes geradoras para os números inteiros positivos da sequência de Leonardo, bem como algumas propriedades inerentes à essas matrizes. Com o viés de realizar o processo de generalização da forma matricial dos números de Leonardo, é então realizada a extensão para o campo dos números inteiros não positivos, na qual, o estudo dessas matrizes é introduzido de forma inédita nesta pesquisa. A forma matricial relaciona as matrizes com os números de Leonardo e ao elevar essas matrizes a n-ésima potência, obtemos algumas novas relações dessa sequência, conhecendo assim os seus respectivos termos

Modular average case analysis: Language implementation and extension

Motivated by accurate average-case analysis, MOdular Quantitative Analysis (MOQA) is developed at the Centre for Efficiency Oriented Languages (CEOL). In essence, MOQA allows the programmer to determine the average running time of a broad class of programmes directly from the code in a (semi-)automated way. The MOQA approach has the property of randomness preservation which means that applying any operation to a random structure, results in an output isomorphic to one or more random structures, which is key to systematic timing. Based on original MOQA research, we discuss the design and implementation of a new domain specific scripting language based on randomness preserving operations and random structures. It is designed to facilitate compositional timing by systematically tracking the distributions of inputs and outputs. The notion of a labelled partial order (LPO) is the basic data type in the language. The programmer uses built-in MOQA operations together with restricted control flow statements to design MOQA programs. This MOQA language is formally specified both syntactically and semantically in this thesis. A practical language interpreter implementation is provided and discussed. By analysing new algorithms and data restructuring operations, we demonstrate the wide applicability of the MOQA approach. Also we extend MOQA theory to a number of other domains besides average-case analysis. We show the strong connection between MOQA and parallel computing, reversible computing and data entropy analysis

PaVo un tri parallèle adaptatif

Gamers are used to throw onto the latest graphics cards to play immersive games which precision, realism and interactivity keep increasing over time. With general-propose processing on graphics processing units, scientists now participate in graphics card use too. First, we examine these architectures interest for large-scale physics simulations. Drawing on this experience, we highlight in particular a bottleneck in simulations performance. Let us consider a typical situation: cracks in complex reinforced concrete structures such as dams are modelised by many particles. Interactions between particles simulate the matter cohesion. In computer memory, each particle is represented by a set of physical parameters used for every force calculations between two particles. Then, to speed up computations, data from particles close in space should be close in memory. Otherwise, the number of cache misses raises up and memory bandwidth may be reached, specially in parallel environments, limiting global performance. The challenge is to maintain data organization during the simulations despite particle movements. Classical sorting algorithms do not suit such situations because they consistently sort all the elements. Besides, they work upon dense structures leading to a lot of memory transfers. We propose PaVo, an adaptive sort which means it benefits from sequence presortedness. Moreover, to reduce the number of necessary memory transfers, PaVo spreads some gaps inside the data structure. We present a large experimental study and confront results to reputed sort algorithms. Reducing memory requests is again more important for large scale simulations with parallel architectures. We detail a parallel version of PaVo and evaluate its interest. To deal with application irregularities, we do load balancing with work-stealing. We take advantage of hierarchical architectures by automatically distributing data in memory. Thus, tasks are pre-assigned to cores with respect to this organization and we adapt the scheduler to favor steals of tasks working on data close in memory.Les joueurs exigeants acquièrent dès que possible une carte graphique capable de satisfaire leur soif d'immersion dans des jeux dont la précision, le réalisme et l'interactivité redoublent d'intensité au fil du temps. Depuis l'avènement des cartes graphiques dédiées au calcul généraliste, ils n'en sont plus les seuls clients. Dans un premier temps, nous analysons l'apport de ces architectures parallèles spécifiques pour des simulations physiques à grande échelle. Cette étude nous permet de mettre en avant un goulot d'étranglement en particulier limitant la performance des simulations. Partons d'un cas typique : les fissures d'une structure complexe de type barrage en béton armé peuvent être modélisées par un ensemble de particules. La cohésion de la matière ainsi simulée est assurée par les interactions entre elles. Chaque particule est représentée en mémoire par un ensemble de paramètres physiques à consulter systématiquement pour tout calcul de forces entre deux particules. Ainsi, pour que les calculs soient rapides, les données de particules proches dans l'espace doivent être proches en mémoire. Dans le cas contraire, le nombre de défauts de cache augmente et la limite de bande passante de la mémoire peut être atteinte, particulièrement en parallèle, bornant les performances. L'enjeu est de maintenir l'organisation des données en mémoire tout au long de la simulation malgré les mouvements des particules. Les algorithmes de tri standard ne sont pas adaptés car ils trient systématiquement tous les éléments. De plus, ils travaillent sur des structures denses ce qui implique de nombreux déplacements de données en mémoire. Nous proposons PaVo, un algorithme de tri dit adaptatif, c'est-à-dire qu'il sait tirer parti de l'ordre pré-existant dans une séquence. De plus, PaVo maintient des trous dans la structure, répartis de manière à réduire le nombre de déplacements mémoires nécessaires. Nous présentons une généreuse étude expérimentale et comparons les résultats obtenus à plusieurs tris renommés. La diminution des accès à la mémoire a encore plus d'importance pour des simulations à grande échelles sur des architectures parallèles. Nous détaillons une version parallèle de PaVo et évaluons son intérêt. Pour tenir compte de l'irrégularité des applications, la charge de travail est équilibrée dynamiquement par vol de travail. Nous proposons de distribuer automatiquement les données en mémoire de manière à profiter des architectures hiérarchiques. Les tâches sont pré-assignées aux cœurs pour utiliser cette distribution et nous adaptons le moteur de vol pour favoriser des vols de tâches concernant des données proches en mémoire

Smoothsort, an alternative for sorting in situ

Like heapsort - which inspired it - smoothsort is an algorithm for sorting in situ. It is of order N · log N in the worst case, but of order N in the best case, with a smooth transition between the two. (Hence its name.

Smoothsort commented transcription EWD796a Smoothsort, an alternative for sorting in situ by Edsger W. Dijkstra

transcribed and commented by Hartwig Thoma