An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

Power-and-area efficient 14-bit 1.5 MSample/s two-stage algorithmic ADC based on a mismatch-insensitive MDAC

IEEE International Symposium on Circuits and Systems, pp. 220 – 223, Seattle, EUA

Algorithmic skeleton framework for the orchestration of GPU computations

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

Multi-GPU support on the marrow algorithmic skeleton framework

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

Heterogeneous computing with an algorithmic skeleton framework

The Graphics Processing Unit (GPU) is present in almost every modern day personal computer. Despite its specific purpose design, they have been increasingly used for general computations with very good results. Hence, there is a growing effort from the community to seamlessly integrate this kind of devices in everyday computing. However, to fully exploit the potential of a system comprising GPUs and CPUs, these devices should be presented to the programmer as a single platform. The efficient combination of the power of CPU and GPU devices is highly dependent on each device’s characteristics, resulting in platform specific applications that cannot be ported to different systems. Also, the most efficient work balance among devices is highly dependable on the computations to be performed and respective data sizes. In this work, we propose a solution for heterogeneous environments based on the abstraction level provided by algorithmic skeletons. Our goal is to take full advantage of the power of all CPU and GPU devices present in a system, without the need for different kernel implementations nor explicit work-distribution.To that end, we extended Marrow, an algorithmic skeleton framework for multi-GPUs, to support CPU computations and efficiently balance the work-load between devices. Our approach is based on an offline training execution that identifies the ideal work balance and platform configurations for a given application and input data size. The evaluation of this work shows that the combination of CPU and GPU devices can significantly boost the performance of our benchmarks in the tested environments, when compared to GPU-only executions.

Towards an algorithmic skeleton framework for programming the Intel R Xeon PhiTM processor

The Intel R Xeon PhiTM is the first processor based on Intel’s MIC (Many Integrated Cores) architecture. It is a co-processor specially tailored for data-parallel computations, whose basic architectural design is similar to the ones of GPUs (Graphics Processing Units), leveraging the use of many integrated low computational cores to perform parallel computations. The main novelty of the MIC architecture, relatively to GPUs, is its compatibility with the Intel x86 architecture. This enables the use of many of the tools commonly available for the parallel programming of x86-based architectures, which may lead to a smaller learning curve. However, programming the Xeon Phi still entails aspects intrinsic to accelerator-based computing, in general, and to the MIC architecture, in particular. In this thesis we advocate the use of algorithmic skeletons for programming the Xeon Phi. Algorithmic skeletons abstract the complexity inherent to parallel programming, hiding details such as resource management, parallel decomposition, inter-execution flow communication, thus removing these concerns from the programmer’s mind. In this context, the goal of the thesis is to lay the foundations for the development of a simple but powerful and efficient skeleton framework for the programming of the Xeon Phi processor. For this purpose we build upon Marrow, an existing framework for the orchestration of OpenCLTM computations in multi-GPU and CPU environments. We extend Marrow to execute both OpenCL and C++ parallel computations on the Xeon Phi. We evaluate the newly developed framework, several well-known benchmarks, like Saxpy and N-Body, will be used to compare, not only its performance to the existing framework when executing on the co-processor, but also to assess the performance on the Xeon Phi versus a multi-GPU environment.

An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

Algorithmic assistance to the optimization process in vehicle routing problems

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2013

Algorithmic aspects of bio-inspired string operations

We present building blocks for algorithms for the efficient reduction of square factor, i.e. direct repetitions in strings. So the basic problem is this: given a string, compute all strings that can be obtained by reducing factors of the form zz to z. Two types of algorithms are treated: an offline algorithm is one that can compute a data structure on the given string in advance before the actual search for the square begins; in contrast, online algorithms receive all input only at the time when a request is made. For offline algorithms we treat the following problem: Let u and w be two strings such that w is obtained from u by reducing a square factor zz to only z. If we further are given the suffix table of u, how can we derive the suffix table for w without computing it from scratch? As the suffix table plays a key role in online algorithms for the detection of squares in a string, this derivation can make the iterated reduction of squares more efficient. On the other hand, we also show how a suffix array, used for the offline detection of squares, can be adapted to the new string resulting from the deletion of a square. Because the deletion is a very local change, this adaption is more eficient than the computation of the new suffix array from scratch.

System-level Support for Mobile Ad hoc Communications: an Algorithmic & Practical Approach

A mobile ad hoc network (MANET) is a decentralized and infrastructure-less network. This thesis aims to provide support at the system-level for developers of applications or protocols in such networks. To do this, we propose contributions in both the algorithmic realm and in the practical realm. In the algorithmic realm, we contribute to the field by proposing different context-aware broadcast and multicast algorithms in MANETs, namely six-shot broadcast, six-shot multicast, PLAN-B and ageneric algorithmic approach to optimize the power consumption of existing algorithms. For each algorithm we propose, we compare it to existing algorithms that are either probabilistic or context-aware, and then we evaluate their performance based on simulations. We demonstrate that in some cases, context-aware information, such as location or signal-strength, can improve the effciency. In the practical realm, we propose a testbed framework, namely ManetLab, to implement and to deploy MANET-specific protocols, and to evaluate their performance. This testbed framework aims to increase the accuracy of performance evaluation compared to simulations, while keeping the ease of use offered by the simulators to reproduce a performance evaluation. By evaluating the performance of different probabilistic algorithms with ManetLab, we observe that both simulations and testbeds should be used in a complementary way. In addition to the above original contributions, we also provide two surveys about system-level support for ad hoc communications in order to establish a state of the art. The first is about existing broadcast algorithms and the second is about existing middleware solutions and the way they deal with privacy and especially with location privacy. - Un réseau mobile ad hoc (MANET) est un réseau avec une architecture décentralisée et sans infrastructure. Cette thèse vise à fournir un support adéquat, au niveau système, aux développeurs d'applications ou de protocoles dans de tels réseaux. Dans ce but, nous proposons des contributions à la fois dans le domaine de l'algorithmique et dans celui de la pratique. Nous contribuons au domaine algorithmique en proposant différents algorithmes de diffusion dans les MANETs, algorithmes qui sont sensibles au contexte, à savoir six-shot broadcast,six-shot multicast, PLAN-B ainsi qu'une approche générique permettant d'optimiser la consommation d'énergie de ces algorithmes. Pour chaque algorithme que nous proposons, nous le comparons à des algorithmes existants qui sont soit probabilistes, soit sensibles au contexte, puis nous évaluons leurs performances sur la base de simulations. Nous montrons que, dans certains cas, des informations liées au contexte, telles que la localisation ou l'intensité du signal, peuvent améliorer l'efficience de ces algorithmes. Sur le plan pratique, nous proposons une plateforme logicielle pour la création de bancs d'essai, intitulé ManetLab, permettant d'implémenter, et de déployer des protocoles spécifiques aux MANETs, de sorte à évaluer leur performance. Cet outil logiciel vise à accroître la précision desévaluations de performance comparativement à celles fournies par des simulations, tout en conservant la facilité d'utilisation offerte par les simulateurs pour reproduire uneévaluation de performance. En évaluant les performances de différents algorithmes probabilistes avec ManetLab, nous observons que simulateurs et bancs d'essai doivent être utilisés de manière complémentaire. En plus de ces contributions principales, nous fournissons également deux états de l'art au sujet du support nécessaire pour les communications ad hoc. Le premier porte sur les algorithmes de diffusion existants et le second sur les solutions de type middleware existantes et la façon dont elles traitent de la confidentialité, en particulier celle de la localisation.

Algorithmic Solutions for Combinatorial Problems in Resource Management of Manufacturing Environments

This thesis studies the use of heuristic algorithms in a number of combinatorial problems that occur in various resource constrained environments. Such problems occur, for example, in manufacturing, where a restricted number of resources (tools, machines, feeder slots) are needed to perform some operations. Many of these problems turn out to be computationally intractable, and heuristic algorithms are used to provide efficient, yet sub-optimal solutions. The main goal of the present study is to build upon existing methods to create new heuristics that provide improved solutions for some of these problems. All of these problems occur in practice, and one of the motivations of our study was the request for improvements from industrial sources. We approach three different resource constrained problems. The first is the tool switching and loading problem, and occurs especially in the assembly of printed circuit boards. This problem has to be solved when an efficient, yet small primary storage is used to access resources (tools) from a less efficient (but unlimited) secondary storage area. We study various forms of the problem and provide improved heuristics for its solution. Second, the nozzle assignment problem is concerned with selecting a suitable set of vacuum nozzles for the arms of a robotic assembly machine. It turns out that this is a specialized formulation of the MINMAX resource allocation formulation of the apportionment problem and it can be solved efficiently and optimally. We construct an exact algorithm specialized for the nozzle selection and provide a proof of its optimality. Third, the problem of feeder assignment and component tape construction occurs when electronic components are inserted and certain component types cause tape movement delays that can significantly impact the efficiency of printed circuit board assembly. Here, careful selection of component slots in the feeder improves the tape movement speed. We provide a formal proof that this problem is of the same complexity as the turnpike problem (a well studied geometric optimization problem), and provide a heuristic algorithm for this problem.

Algorithmic Techniques in Gene Expression Processing. From Imputation to Visualization

The amount of biological data has grown exponentially in recent decades. Modern biotechnologies, such as microarrays and next-generation sequencing, are capable to produce massive amounts of biomedical data in a single experiment. As the amount of the data is rapidly growing there is an urgent need for reliable computational methods for analyzing and visualizing it. This thesis addresses this need by studying how to efficiently and reliably analyze and visualize high-dimensional data, especially that obtained from gene expression microarray experiments. First, we will study the ways to improve the quality of microarray data by replacing (imputing) the missing data entries with the estimated values for these entries. Missing value imputation is a method which is commonly used to make the original incomplete data complete, thus making it easier to be analyzed with statistical and computational methods. Our novel approach was to use curated external biological information as a guide for the missing value imputation. Secondly, we studied the effect of missing value imputation on the downstream data analysis methods like clustering. We compared multiple recent imputation algorithms against 8 publicly available microarray data sets. It was observed that the missing value imputation indeed is a rational way to improve the quality of biological data. The research revealed differences between the clustering results obtained with different imputation methods. On most data sets, the simple and fast k-NN imputation was good enough, but there were also needs for more advanced imputation methods, such as Bayesian Principal Component Algorithm (BPCA). Finally, we studied the visualization of biological network data. Biological interaction networks are examples of the outcome of multiple biological experiments such as using the gene microarray techniques. Such networks are typically very large and highly connected, thus there is a need for fast algorithms for producing visually pleasant layouts. A computationally efficient way to produce layouts of large biological interaction networks was developed. The algorithm uses multilevel optimization within the regular force directed graph layout algorithm.

Interpreting Quantifier Scope Ambiguity: Evidence of Heuristic First, Algorithmic Second Processing

The present work suggests that sentence processing requires both heuristic and algorithmic processing streams, where the heuristic processing strategy precedes the algorithmic phase. This conclusion is based on three self-paced reading experiments in which the processing of two-sentence discourses was investigated, where context sentences exhibited quantifier scope ambiguity. Experiment 1 demonstrates that such sentences are processed in a shallow manner. Experiment 2 uses the same stimuli as Experiment 1 but adds questions to ensure deeper processing. Results indicate that reading times are consistent with a lexical-pragmatic interpretation of number associated with context sentences, but responses to questions are consistent with the algorithmic computation of quantifier scope. Experiment 3 shows the same pattern of results as Experiment 2, despite using stimuli with different lexicalpragmatic biases. These effects suggest that language processing can be superficial, and that deeper processing, which is sensitive to structure, only occurs if required. Implications for recent studies of quantifier scope ambiguity are discussed.

Algorithmic Computation of Formal Fourier Series

KAAD (Katholischer Akademischer Ausländer-Dienst)

An algorithmic approach for collaborative-based prediction of user contexts in ubiquitous environments under consideration of legal implications

Mit Hilfe der Vorhersage von Kontexten können z. B. Dienste innerhalb einer ubiquitären Umgebung proaktiv an die Bedürfnisse der Nutzer angepasst werden. Aus diesem Grund hat die Kontextvorhersage einen signifikanten Stellenwert innerhalb des ’ubiquitous computing’. Nach unserem besten Wissen, verwenden gängige Ansätze in der Kontextvorhersage ausschließlich die Kontexthistorie des Nutzers als Datenbasis, dessen Kontexte vorhersagt werden sollen. Im Falle, dass ein Nutzer unerwartet seine gewohnte Verhaltensweise ändert, enthält die Kontexthistorie des Nutzers keine geeigneten Informationen, um eine zuverlässige Kontextvorhersage zu gewährleisten. Daraus folgt, dass Vorhersageansätze, die ausschließlich die Kontexthistorie des Nutzers verwenden, dessen Kontexte vorhergesagt werden sollen, fehlschlagen könnten. Um die Lücke der fehlenden Kontextinformationen in der Kontexthistorie des Nutzers zu schließen, führen wir den Ansatz zur kollaborativen Kontextvorhersage (CCP) ein. Dabei nutzt CCP bestehende direkte und indirekte Relationen, die zwischen den Kontexthistorien der verschiedenen Nutzer existieren können, aus. CCP basiert auf der Singulärwertzerlegung höherer Ordnung, die bereits erfolgreich in bestehenden Empfehlungssystemen eingesetzt wurde. Um Aussagen über die Vorhersagegenauigkeit des CCP Ansatzes treffen zu können, wird dieser in drei verschiedenen Experimenten evaluiert. Die erzielten Vorhersagegenauigkeiten werden mit denen von drei bekannten Kontextvorhersageansätzen, dem ’Alignment’ Ansatz, dem ’StatePredictor’ und dem ’ActiveLeZi’ Vorhersageansatz, verglichen. In allen drei Experimenten werden als Evaluationsbasis kollaborative Datensätze verwendet. Anschließend wird der CCP Ansatz auf einen realen kollaborativen Anwendungsfall, den proaktiven Schutz von Fußgängern, angewendet. Dabei werden durch die Verwendung der kollaborativen Kontextvorhersage Fußgänger frühzeitig erkannt, die potentiell Gefahr laufen, mit einem sich nähernden Auto zu kollidieren. Als kollaborative Datenbasis werden reale Bewegungskontexte der Fußgänger verwendet. Die Bewegungskontexte werden mittels Smartphones, welche die Fußgänger in ihrer Hosentasche tragen, gesammelt. Aus dem Grund, dass Kontextvorhersageansätze in erster Linie personenbezogene Kontexte wie z.B. Standortdaten oder Verhaltensmuster der Nutzer als Datenbasis zur Vorhersage verwenden, werden rechtliche Evaluationskriterien aus dem Recht des Nutzers auf informationelle Selbstbestimmung abgeleitet. Basierend auf den abgeleiteten Evaluationskriterien, werden der CCP Ansatz und weitere bekannte kontextvorhersagende Ansätze bezüglich ihrer Rechtsverträglichkeit untersucht. Die Evaluationsergebnisse zeigen die rechtliche Kompatibilität der untersuchten Vorhersageansätze bezüglich des Rechtes des Nutzers auf informationelle Selbstbestimmung auf. Zum Schluss wird in der Dissertation ein Ansatz für die verteilte und kollaborative Vorhersage von Kontexten vorgestellt. Mit Hilfe des Ansatzes wird eine Möglichkeit aufgezeigt, um den identifizierten rechtlichen Probleme, die bei der Vorhersage von Kontexten und besonders bei der kollaborativen Vorhersage von Kontexten, entgegenzuwirken.