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DTSTART;TZID=Europe/Paris:20190312T140000
DTEND;TZID=Europe/Paris:20190312T170000
DTSTAMP:20190312T144501Z
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SUMMARY:PhD Defense - Iordan Iordanov (team Gamble)
DESCRIPTION:Iordan Iordanov\, PhD student in Gamble team will defense his thesis entitled « Delaunay triangulations of a family of symmetric hyperbolic surfaces in practice ». The defense is planned for Tuesday\, 12 March 2019 in room C005 at 14h00.\n\nAbstract :\n\n\nThe Bolza surface is the most symmetric compact orientable hyperbolic surface of genus 2. For any genus higher than 2\, there exists one compact orientable surface constructed in a similar way as the Bolza surface having the same kind of symmetry. We refer to this family of surfaces as symmetric hyperbolic surfaces. This thesis deals with the computation of Delaunay triangulations of symmetric hyperbolic surfaces.\nDelaunay triangulations of compact surfaces can be seen as periodic Delaunay triangulations of their universal cover (in our case\, the hyperbolic plane). A Delaunay triangulation is for us a simplicial complex. However\, not all sets of points define a simplicial decomposition of a symmetric hyperbolic surface. In the literature\, an algorithm has been proposed to deal with this issue by using so-called dummy points: initially a triangulation of the surface is constructed with a set of dummy points that defines a Delaunay triangulation of the surface\, then input points are inserted with the well- known incremental algorithm by Bowyer\, and finally the dummy points are removed\, if the triangulation remains a simplicial complex after their removal. For the Bolza surface\, the set of dummy points to initialize the triangulation is given. The existing algorithm computes a triangulation of the Bolza surface as a periodic triangulation of the hyperbolic plane and requires to identify a suitable subset of the hyperbolic plane in which to work.\nWe study the properties of Delaunay triangulations of the Bolza surface defined by sets of points containing the proposed set of dummy points\, and we describe in detail an implementation of the incremental algorithm for it. We begin by identifying a subset of the hyperbolic plane that contains at least one representative for each face of a Delaunay triangulation of the surface\, which enables us to define a unique canonical representative\niiin the hyperbolic plane for each face on the surface. We give a data structure to represent a Delaunay triangulation of the Bolza surface via the canonical representatives of its faces in the hyperbolic plane. We detail the construction of such a triangulation and additional operations that enable the location of points and the removal of vertices. We also report results on the algebraic degree of predicates needed for all operations.\nWe provide a fully dynamic implementation for the Bolza surface\, supporting insertion of new points\, removal of existing vertices\, point location\, and construction of dual objects. Our implementation is based on CGAL\, the Computational Geometry Algorithms Library\, and is currently under revision for integration in the library. To incorporate our code into CGAL\, all the objects that we introduce must be compatible with the existing framework and comply with the standards adopted by the library. We give a detailed description of the classes used to represent and handle periodic hyperbolic triangulations and related objects. Benchmarks and tests are performed to evaluate our implementation\, and a simple application is given in the form of a CGAL demo.\nWe discuss an extension of our implementation to symmetric hyperbolic surfaces of genus higher than 2. We propose three methods to generate sets of dummy points for each surface and present the advantages and shortcomings of each method. We identify a suitable subset of the hyperbolic plane that contains at least one representative for each face of a Delaunay triangulation of the surface\, and we define a canonical representative in the hyperbolic plane for each face on the surface. We describe a data structure to represent such a triangulation via the canonical representatives of its faces\, and give algorithms for the initialization of the triangulation with dummy points. Finally\, we discuss a preliminary implementation in which we examine the difficulties of having efficient exact predicates for the construction of Delaunay triangulations of symmetric hyperbolic surfaces.
URL:https://www.loria.fr/event/phd-defense-jordan-iordanov-team-gamble/
CATEGORIES:Soutenance
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DTSTART;TZID=Europe/Paris:20190319T100000
DTEND;TZID=Europe/Paris:20190319T120000
DTSTAMP:20190314T154615Z
CREATED:20190314T154615Z
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SUMMARY:PhD defense : Meihui Gao
DESCRIPTION:Meihui Gar will defekt her thesis on Tuesday\, 19 March at 10h00 in room A008. \nHer presentation is entitled « Models and Methods for Network Function Virtualization (NFV) Architectures ». \nJury:\n\nPr.  Bernard FORTZ                        (Université Libre de Bruxelles)                                Rapporteur / Reviewer\nPr.  Luigi DE GIOVANNI                 (Università degli Studi di Padova)                          Rapporteur / Reviewer\nPr.  Stefano SECCI                          (Conservatoire national des arts et métiers)         Examinatuer / Examiner\n\nDr.  Éric GOURDIN                          (Orange Gardens)                                                     Examinateur / Examiner\n\nPr.  Bernardetta ADDIS                   (Université de Lorraine)                                           Co-directeur de thèse / Co-supervisor\nPr.  Ye Qiong SONG                        (Université de Lorraine)                                           Directeur de thèse / Supervisor\n\n\nAbstract:\nDue to the exponential growth of service demands\, telecommunication networks are populated with a large and increasing variety of proprietary hardware appliances\, increasing the cost and the complexity of the network management. The NFV paradigm is proposed to overcome this problem\, allowing dynamical allocation of Virtual Network Functions (VNFs) to make network function provision and operation more flexible and cost-effective. A key problem in NFV is the NFV service chaining: given a network where some nodes are connected with computational servers and a set of demands asking for network services composed of a sequence of VNF instances. VNF instances need to be installed on servers and the demands must be routed in such a way that each demand accesses the requested VNFs. Despite thelarge number of research papers\, little has been done towards achieving cost-efficient VNFs Placement and demands Routing (VNF-PR). From an optimization point of view\, the problem can be modeled as the combination of a facility location problem (for the VNF location and server dimensioning) and a network design problem (for the demands routing). Both problems are widely studied in the literature\, but their combination represent a new challenge. \n\nIn this thesis\, we focus on the VNF-PR problem. Our objective is to study the problem structure and features\, analyze and compare the most promising formulations\, and finally propose exact and heuristic methods to solve efficiently the problem. In the first stage\, we study the VNF-PR problem structures and features. For this\, we extend the work in [1] by considering more realistic features and constraints of NFV infrastructures and we propose a linear programming model to solve it. Then\, we design a math-heuristic algorithm to scale with multiple objectives\, which allows us to study further the mutual impact between classical traffic engineering and NFV infrastructures efficiency goals. We generate scenarios with different VNF forwarding profiles\, different cases of demand distribution and different levels of end-to-end latency bound to evaluate the proposed method. Computational results show that our method can provide a stable and close-to-optimum solution for the considered problem and there is a trade-off achievable between classical traffic engineering and NFV infrastructures cost-efficiency goals. In the second stage\, our goal is to investigate the problem complexity and properties and to analyze and compare different mathematical programming models. To do so\, we move into the theoretical part of the problem. We formalize a simplified\, yet significant variant\, the VNF-PR with simple path routing (VNF-PR SP ) problem. We prove the NP-completeness of the VNF-PR SP problem. Further\, we derive problem properties and use them to help in speeding up the optimization. In order to better understand the behavior of different mathematical programming models\, we generate a common test bed with more than 100 different test instances under different capacity settings and topology features\, on which we evaluate and compare the two most promising formulations (i.e.\, PR and SP) proposed in the literature. We prove both theoretically and computationally that the continuous relaxation of SP always provides a bound no worse than the one of PR. Then\, we introduce additional inequalities to strengthen the formulations\, and we extend the formulations to address more general versions of the problem with multiple VNF types and multiple orders. Finally\, we address the problem scalability by proposing exact and heuristic methods to deal with large size instances (with up to 60 nodes and 1800 demands) of the VNF-PR SP problem. In our exact methods\, we partially fix the solution and solve the model to complete it. In our heuristic methods\, we combine the mathematical programming models with a local search technique\, which allows us to explore quickly the reduced solution space to provide a feasible solution. We show that: our exact methods can solve efficiently (e.g.\, less than 2 seconds under some capacity cases) the small size instances (with less than 30 nodes and 300 demands) of the problem; our proposed heuristic methods can solve efficiently medium size instances (with between 20 and 30 nodes\, 300 and 1000 demands) of challenging capacity cases and provide feasible solutions for large size instances of the most difficult capacity cases\, for which the models cannot find any feasible solution even with large computational time (i.e.\, 2hours).\n\nKeywords: Network Function Virtualization (NFV)\, Resource Allocation\, Operations Research
URL:https://www.loria.fr/event/phd-defense-meihui-gao/
CATEGORIES:Soutenance
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