1,768 research outputs found

    Graph Searching, Elimination Trees, and a Generalization of Bandwidth

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    Combinatorial problems in solving linear systems

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    42 pages, available as LIP research report RR-2009-15Numerical linear algebra and combinatorial optimization are vast subjects; as is their interaction. In virtually all cases there should be a notion of sparsity for a combinatorial problem to arise. Sparse matrices therefore form the basis of the interaction of these two seemingly disparate subjects. As the core of many of today's numerical linear algebra computations consists of the solution of sparse linear system by direct or iterative methods, we survey some combinatorial problems, ideas, and algorithms relating to these computations. On the direct methods side, we discuss issues such as matrix ordering; bipartite matching and matrix scaling for better pivoting; task assignment and scheduling for parallel multifrontal solvers. On the iterative method side, we discuss preconditioning techniques including incomplete factorization preconditioners, support graph preconditioners, and algebraic multigrid. In a separate part, we discuss the block triangular form of sparse matrices

    Graph-theoretic Approach To Modeling Propagation And Control Of Network Worms

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    In today\u27s network-dependent society, cyber attacks with network worms have become the predominant threat to confidentiality, integrity, and availability of network computing resources. Despite ongoing research efforts, there is still no comprehensive network-security solution aimed at controling large-scale worm propagation. The aim of this work is fivefold: (1) Developing an accurate combinatorial model of worm propagation that can facilitate the analysis of worm control strategies, (2) Building an accurate epidemiological model for the propagation of a worm employing local strategies, (3) Devising distributed architecture and algorithms for detection of worm scanning activities, (4) Designing effective control strategies against the worm, and (5) Simulation of the developed models and strategies on large, scale-free graphs representing real-world communication networks. The proposed pair-approximation model uses the information about the network structure--order, size, degree distribution, and transitivity. The empirical study of propagation on large scale-free graphs is in agreement with the theoretical analysis of the proposed pair-approximation model. We, then, describe a natural generalization of the classical cops-and-robbers game--a combinatorial model of worm propagation and control. With the help of this game on graphs, we show that the problem of containing the worm is NP-hard. Six novel near-optimal control strategies are devised: combination of static and dynamic immunization, reactive dynamic and invariant dynamic immunization, soft quarantining, predictive traffic-blocking, and contact-tracing. The analysis of the predictive dynamic traffic-blocking, employing only local information, shows that the worm can be contained so that 40\% of the network nodes are not affected. Finally, we develop the Detection via Distributed Blackholes architecture and algorithm which reflect the propagation strategy used by the worm and the salient properties of the network. Our distributed detection algorithm can detect the worm scanning activity when only 1.5% of the network has been affected by the propagation. The proposed models and algorithms are analyzed with an individual-based simulation of worm propagation on realistic scale-free topologies

    Multi-objective optimization in graphical models

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    Many real-life optimization problems are combinatorial, i.e. they concern a choice of the best solution from a finite but exponentially large set of alternatives. Besides, the solution quality of many of these problems can often be evaluated from several points of view (a.k.a. criteria). In that case, each criterion may be described by a different objective function. Some important and well-known multicriteria scenarios are: · In investment optimization one wants to minimize risk and maximize benefits. · In travel scheduling one wants to minimize time and cost. · In circuit design one wants to minimize circuit area, energy consumption and maximize speed. · In knapsack problems one wants to minimize load weight and/or volume and maximize its economical value. The previous examples illustrate that, in many cases, these multiple criteria are incommensurate (i.e., it is difficult or impossible to combine them into a single criterion) and conflicting (i.e., solutions that are good with respect one criterion are likely to be bad with respect to another). Taking into account simultaneously the different criteria is not trivial and several notions of optimality have been proposed. Independently of the chosen notion of optimality, computing optimal solutions represents an important current research challenge. Graphical models are a knowledge representation tool widely used in the Artificial Intelligence field. They seem to be specially suitable for combinatorial problems. Roughly, graphical models are graphs in which nodes represent variables and the (lack of) arcs represent conditional independence assumptions. In addition to the graph structure, it is necessary to specify its micro-structure which tells how particular combinations of instantiations of interdependent variables interact. The graphical model framework provides a unifying way to model a broad spectrum of systems and a collection of general algorithms to efficiently solve them. In this Thesis we integrate multi-objective optimization problems into the graphical model paradigm and study how algorithmic techniques developed in the graphical model context can be extended to multi-objective optimization problems. As we show, multiobjective optimization problems can be formalized as a particular case of graphical models using the semiring-based framework. It is, to the best of our knowledge, the first time that graphical models in general, and semiring-based problems in particular are used to model an optimization problem in which the objective function is partially ordered. Moreover, we show that most of the solving techniques for mono-objective optimization problems can be naturally extended to the multi-objective context. The result of our work is the mathematical formalization of multi-objective optimization problems and the development of a set of multiobjective solving algorithms that have been proved to be efficient in a number of benchmarks.Muchos problemas reales de optimización son combinatorios, es decir, requieren de la elección de la mejor solución (o solución óptima) dentro de un conjunto finito pero exponencialmente grande de alternativas. Además, la mejor solución de muchos de estos problemas es, a menudo, evaluada desde varios puntos de vista (también llamados criterios). Es este caso, cada criterio puede ser descrito por una función objetivo. Algunos escenarios multi-objetivo importantes y bien conocidos son los siguientes: · En optimización de inversiones se pretende minimizar los riesgos y maximizar los beneficios. · En la programación de viajes se quiere reducir el tiempo de viaje y los costes. · En el diseño de circuitos se quiere reducir al mínimo la zona ocupada del circuito, el consumo de energía y maximizar la velocidad. · En los problemas de la mochila se quiere minimizar el peso de la carga y/o el volumen y maximizar su valor económico. Los ejemplos anteriores muestran que, en muchos casos, estos criterios son inconmensurables (es decir, es difícil o imposible combinar todos ellos en un único criterio) y están en conflicto (es decir, soluciones que son buenas con respecto a un criterio es probable que sean malas con respecto a otra). Tener en cuenta de forma simultánea todos estos criterios no es trivial y para ello se han propuesto diferentes nociones de optimalidad. Independientemente del concepto de optimalidad elegido, el cómputo de soluciones óptimas representa un importante desafío para la investigación actual. Los modelos gráficos son una herramienta para la represetanción del conocimiento ampliamente utilizados en el campo de la Inteligencia Artificial que parecen especialmente indicados en problemas combinatorios. A grandes rasgos, los modelos gráficos son grafos en los que los nodos representan variables y la (falta de) arcos representa la interdepencia entre variables. Además de la estructura gráfica, es necesario especificar su (micro-estructura) que indica cómo interactúan instanciaciones concretas de variables interdependientes. Los modelos gráficos proporcionan un marco capaz de unificar el modelado de un espectro amplio de sistemas y un conjunto de algoritmos generales capaces de resolverlos eficientemente. En esta tesis integramos problemas de optimización multi-objetivo en el contexto de los modelos gráficos y estudiamos cómo diversas técnicas algorítmicas desarrolladas dentro del marco de los modelos gráficos se pueden extender a problemas de optimización multi-objetivo. Como mostramos, este tipo de problemas se pueden formalizar como un caso particular de modelo gráfico usando el paradigma basado en semi-anillos (SCSP). Desde nuestro conocimiento, ésta es la primera vez que los modelos gráficos en general, y el paradigma basado en semi-anillos en particular, se usan para modelar un problema de optimización cuya función objetivo está parcialmente ordenada. Además, mostramos que la mayoría de técnicas para resolver problemas monoobjetivo se pueden extender de forma natural al contexto multi-objetivo. El resultado de nuestro trabajo es la formalización matemática de problemas de optimización multi-objetivo y el desarrollo de un conjunto de algoritmos capaces de resolver este tipo de problemas. Además, demostramos que estos algoritmos son eficientes en un conjunto determinado de benchmarks

    Maintaining Quality of Service for Adaptive Mobile Map Clients

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    Mobile devices must deal with limited and dynamically varying resources, in particular, the network quality of service (QoS). In addition, wireless devices have other constraints such as limited memory, battery power, and physical dimensions. Applications that execute in such environments need to adapt to the dynamic operating conditions in order to preserve an acceptable level of service as close to 100% of the time as possible. Viewing and downloading digital spatial data on mobile devices has become more popular, especially with the availability of location-aware applications that exploit GPS (Global Positioning System) receivers integrated in many of today's mobile devices. Map client applications face many challenges in accessing data across a wireless network. Vector spatial data files tend to be large, and file sizes tend to increase unpredictably depending on the complexity of feature geometry. Due to the limited size of the mobile device display, viewing all the details of the map could cause unreasonable clutter and render the map useless. Even if it is feasible to transmit all the details from a QoS standpoint, this could pose a problem from a usability standpoint. This research effort aims to tackle the issues of QoS and usability on mobile devices through a client-proxy-server model where clients are on mobile devices. The proxy performs two functions. First, it supplies the client with vital data about the status of the system that allows the client to take adaptive decisions aimed at maintaining the QoS. Second, it performs the adaptive actions requested by the client. There are two types of adaptive actions performed by the proxy, activating and deactivating filters. When filters are activated, the amount of data transmitted from the server to the client is reduced. The client may decide to activate one or more filters either to maintain QoS or to limit clutter on the screen and enhance usability. The map client-server application and the proxy were developed in Java (tm), and a number of experiments and real-life scenarios were designed to determine the effectiveness and feasibility of the proposed adaptation model and to evaluate the performance of the proxy

    Abstraction and cartographic generalization of geographic user-generated content: use-case motivated investigations for mobile users

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    On a daily basis, a conventional internet user queries different internet services (available on different platforms) to gather information and make decisions. In most cases, knowingly or not, this user consumes data that has been generated by other internet users about his/her topic of interest (e.g. an ideal holiday destination with a family traveling by a van for 10 days). Commercial service providers, such as search engines, travel booking websites, video-on-demand providers, food takeaway mobile apps and the like, have found it useful to rely on the data provided by other users who have commonalities with the querying user. Examples of commonalities are demography, location, interests, internet address, etc. This process has been in practice for more than a decade and helps the service providers to tailor their results based on the collective experience of the contributors. There has been also interest in the different research communities (including GIScience) to analyze and understand the data generated by internet users. The research focus of this thesis is on finding answers for real-world problems in which a user interacts with geographic information. The interactions can be in the form of exploration, querying, zooming and panning, to name but a few. We have aimed our research at investigating the potential of using geographic user-generated content to provide new ways of preparing and visualizing these data. Based on different scenarios that fulfill user needs, we have investigated the potential of finding new visual methods relevant to each scenario. The methods proposed are mainly based on pre-processing and analyzing data that has been offered by data providers (both commercial and non-profit organizations). But in all cases, the contribution of the data was done by ordinary internet users in an active way (compared to passive data collections done by sensors). The main contributions of this thesis are the proposals for new ways of abstracting geographic information based on user-generated content contributions. Addressing different use-case scenarios and based on different input parameters, data granularities and evidently geographic scales, we have provided proposals for contemporary users (with a focus on the users of location-based services, or LBS). The findings are based on different methods such as semantic analysis, density analysis and data enrichment. In the case of realization of the findings of this dissertation, LBS users will benefit from the findings by being able to explore large amounts of geographic information in more abstract and aggregated ways and get their results based on the contributions of other users. The research outcomes can be classified in the intersection between cartography, LBS and GIScience. Based on our first use case we have proposed the inclusion of an extended semantic measure directly in the classic map generalization process. In our second use case we have focused on simplifying geographic data depiction by reducing the amount of information using a density-triggered method. And finally, the third use case was focused on summarizing and visually representing relatively large amounts of information by depicting geographic objects matched to the salient topics emerged from the data

    Local search engine with global content based on domain specific knowledge

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    In the growing need for information we have come to rely on search engines. The use of large scale search engines, such as Google, is as common as surfingthe World Wide Web. We are impressed with the capabilities of these search engines but still there is a need for improvment. A common problem withsearching is the ambiguity of words. Their meaning often depends on the context in which they are used or varies across specific domains. To resolve this we propose a domain specific search engine that is globally oriented. We intend to provide content classification according to the target domain concepts, access to privileged information, personalization and custom rankingfunctions. Domain specific concepts have been formalized in the form ofontology. The paper describes our approach to a centralized search service for domain specific content. The approach uses automated indexing for various content sources that can be found in the form of a relational database, we! b service, web portal or page, various document formats and other structured or unstructured data. The gathered data is tagged with various approaches and classified against the domain classification. The indexed data is accessible through a highly optimized and personalized search service
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