497 research outputs found
A Backtracking-Based Algorithm for Computing Hypertree-Decompositions
Hypertree decompositions of hypergraphs are a generalization of tree
decompositions of graphs. The corresponding hypertree-width is a measure for
the cyclicity and therefore tractability of the encoded computation problem.
Many NP-hard decision and computation problems are known to be tractable on
instances whose structure corresponds to hypergraphs of bounded
hypertree-width. Intuitively, the smaller the hypertree-width, the faster the
computation problem can be solved. In this paper, we present the new
backtracking-based algorithm det-k-decomp for computing hypertree
decompositions of small width. Our benchmark evaluations have shown that
det-k-decomp significantly outperforms opt-k-decomp, the only exact hypertree
decomposition algorithm so far. Even compared to the best heuristic algorithm,
we obtained competitive results as long as the hypergraphs are not too large.Comment: 19 pages, 6 figures, 3 table
Gene Regulatory Network Reconstruction Using Bayesian Networks, the Dantzig Selector, the Lasso and Their Meta-Analysis
Modern technologies and especially next generation sequencing facilities are giving a cheaper access to genotype and genomic data measured on the same sample at once. This creates an ideal situation for multifactorial experiments designed to infer gene regulatory networks. The fifth âDialogue for Reverse Engineering Assessments and Methodsâ (DREAM5) challenges are aimed at assessing methods and associated algorithms devoted to the inference of biological networks. Challenge 3 on âSystems Geneticsâ proposed to infer causal gene regulatory networks from different genetical genomics data sets. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis of predicted networks in terms of structure and reliability. The developed meta-analysis was ranked first among the teams participating in Challenge 3A. It paves the way for future extensions of our inference method and more accurate gene network estimates in the context of genetical genomics
Context Selection on Attributed Graphs for Outlier and Community Detection
Today\u27s applications store large amounts of complex data that combine information of different types. Attributed graphs are an example for such a complex database where each object is characterized by its relationships to other objects and its individual properties. Specifically, each node in an attributed graph may be characterized by a large number of attributes. In this thesis, we present different approaches for mining such high dimensional attributed graphs
Pulse propagation, graph cover, and packet forwarding
We study distributed systems, with a particular focus on graph problems and fault tolerance. Fault-tolerance in a microprocessor or even System-on-Chip can be improved by using a fault-tolerant pulse propagation design. The existing design TRIX achieves this goal by being a distributed system consisting of very simple nodes. We show that even in the typical mode of operation without faults, TRIX performs significantly better than a regular wire or clock tree: Statistical evaluation of our simulated experiments show that we achieve a skew with standard deviation of O(log log H), where H is the height of the TRIX grid. The distance-r generalization of classic graph problems can give us insights on how distance affects hardness of a problem. For the distance-r dominating set problem, we present both an algorithmic upper and unconditional lower bound for any graph class with certain high-girth and sparseness criteria. In particular, our algorithm achieves a O(r¡f(r))-approximation in time O(r), where f is the expansion function, which correlates with density. For constant r, this implies a constant approximation factor, in constant time. We also show that no algorithm can achieve a (2r + 1 â δ)-approximation for any δ > 0 in time O(r), not even on the class of cycles of girth at least 5r. Furthermore, we extend the algorithm to related graph cover problems and even to a different execution model. Furthermore, we investigate the problem of packet forwarding, which addresses the question of how and when best to forward packets in a distributed system. These packets are injected by an adversary. We build on the existing algorithm OED to handle more than a single destination. In particular, we show that buffers of size O(log n) are sufficient for this algorithm, in contrast to O(n) for the naive approach.Wir untersuchen verteilte Systeme, mit besonderem Augenmerk auf Graphenprobleme und Fehlertoleranz. Fehlertoleranz auf einem System-on-Chip (SoC) kann durch eine fehlertolerante Puls- Weiterleitung verbessert werden. Das bestehende Puls-Weiterleitungs-System TRIX toleriert Fehler indem es ein verteiltes System ist das nur aus sehr einfachen Knoten besteht. Wir zeigen dass selbst im typischen, fehlerfreien Fall TRIX sich weitaus besser verhält als man naiverweise erwarten wĂźrde: Statistische Analysen unserer simulierten Experimente zeigen, dass der VerzĂśgerungs-Unterschied eine Standardabweichung von lediglich O(log logH) erreicht, wobei H die HĂśhe des TRIX-Netzes ist. Das Generalisieren einiger klassischer Graphen-Probleme auf Distanz r kann uns neue Erkenntnisse bescheren Ăźber den Zusammenhang zwischen Distanz und Komplexität eines Problems. FĂźr das Problem der dominierenden Mengen auf Distanz r zeigen wir sowohl eine algorithmische obere Schranke als auch eine bedingungsfreie untere Schranke fĂźr jede Klasse von Graphen, die bestimmte Eigenschaften an Umfang und Dichte erfĂźllt. Konkret erreicht unser Algorithmus in Zeit O(r) eine AnnäherungsgĂźte von O(r ¡ f(r)). FĂźr konstante r bedeutet das, dass der Algorithmus in konstanter Zeit eine Annäherung konstanter GĂźte erreicht. Weiterhin zeigen wir, dass kein Algorithmus in Zeit O(r) eine AnnäherungsgĂźte besser als 2r + 1 erreichen kann, nicht einmal in der Klasse der Kreis-Graphen von Umfang mindestens 5r. Weiterhin haben wir das Paketweiterleitungs-Problem untersucht, welches sich mit der Frage beschäftigt, wann genau Pakete in einem verteilten System idealerweise weitergeleitetwerden sollten. Die Paketewerden dabei von einem Gegenspieler eingefĂźgt. Wir bauen auf dem existierenden Algorithmus OED auf, um mehr als ein Paket-Ziel beliefern zu kĂśnnen. Dadurch zeigen wir, dass Paket-Speicher der GrĂśĂe O(log n) fĂźr dieses Problem ausreichen, im Gegensatz zu den Paket-Speichern der GrĂśĂe O(n) die fĂźr einen naiven Ansatz nĂśtig wären
Theoretical investigation of malaria prevalence in two Indian cities using the response surface method
<p>Abstract</p> <p>Background</p> <p>Elucidation of the relationships between malaria incidence and climatic and non-climatic factors in a region is of utmost importance in understanding the causative factors of disease spread and design of control strategies. Very often malaria prevalence data is restricted to short time scales (months to few years). This demands application of rigorous statistical modelling techniques for analysis and prediction. The monthly malaria prevalence data for three to five years from two cities in southern India, situated in two different climatic zones, are studied to capture their dependence on climatic factors.</p> <p>Methods</p> <p>The statistical technique of response surface method (RSM) is applied for the first time to study any epidemiological data. A new step-by-step model reduction technique is proposed to refine the initial model obtained from RSM. This provides a simpler structure and gives better fit. This combined approach is applied to two types of epidemiological data (Slide Positivity Rates values and Total Malaria cases), for two cities in India with varying strengths of disease prevalence and environmental conditions.</p> <p>Results</p> <p>The study on these data sets reveals that RSM can be used successfully to elucidate the important environmental factors influencing the transmission of the disease by analysing short epidemiological time series. The proposed approach has high predictive ability over relatively long time horizons.</p> <p>Conclusions</p> <p>This method promises to provide reliable forecast of malaria incidence across varying environmental conditions, which may help in designing useful control programmes for malaria.</p
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