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3rd Brazilian Conference on Intelligent Systems (BRACIS)

作者： Valejo, Alan Valverde-Rebaza, Jorge Lopes, Alneu de Andrade Univ Sao Paulo ICMC Dept Comp Sci BR-13560970 Sao Carlos SP Brazil

ISBN: (纸本)9781479978595

Many real world complex networks have an a overlapping community structure, in which a vertex belongs to one or more communities. Numerous approaches for crisp overlapping community detection were proposed in the literature, most of them have a good accuracy but their computational costs are considerably high and infeasible for large-scale networks. Since the multilevel approach has not been previously applied to deal with overlapping communities detection problem, in this paper we propose an adaptation of this approach to tackle the detection problem to overlapping communities case. The goal is to analyze the time impact and the quality of solution of our multilevel strategy regarding to traditional algorithms. Our experiments show that our proposal consistently produces good performance compared to single-level algorithms and in less time.

关键词： Complex networks Community detection Overlapping community multilevel algorithms

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Scalable and Accurate Graph Clustering and Community Structure Detection

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2013年第5期24卷 1022-1029页

作者： Djidjev, Hristo N. Onus, Melih Los Alamos Natl Lab Los Alamos NM 87545 USA Cankaya Univ Dept Comp Engn TR-06810 Ankara Turkey

One of the most useful measures of cluster quality is the modularity of the partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random graph. In this paper, we show that the problem of finding a partition maximizing the modularity of a given graph G can be reduced to a minimum weighted cut (MWC) problem on a complete graph with the same vertices as G. We then show that the resulting minimum cut problem can be efficiently solved by adapting existing graph partitioning techniques. Our algorithm finds clusterings of a comparable quality and is much faster than the existing clustering algorithms.

关键词： Graph clustering community detection graph partitioning multilevel algorithms modularity

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Adaptive-multilevel BDDC and its parallel implementation

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COMPUTING 2013年第12期95卷 1087-1119页

作者： Sousedik, Bedrich Sistek, Jakub Mandel, Jan Univ So Calif Dept Aerosp & Mech Engn Los Angeles CA 90089 USA Acad Sci Czech Republ Inst Thermomech CZ-18200 Prague 8 Czech Republic Acad Sci Czech Republ Inst Math CR-11567 Prague 1 Czech Republic Univ Colorado Dept Math & Stat Sci Denver CO 80217 USA

We combine the adaptive and multilevel approaches to the BDDC and formulate a method which allows an adaptive selection of constraints on each decomposition level. We also present a strategy for the solution of local eigenvalue problems in the adaptive algorithm using the LOBPCG method with a preconditioner based on standard components of the BDDC. The effectiveness of the method is illustrated on several engineering problems. It appears that the Adaptive-multilevel BDDC algorithm is able to effectively detect troublesome parts on each decomposition level and improve convergence of the method. The developed open-source parallel implementation shows a good scalability as well as applicability to very large problems and core counts.

关键词： Parallel algorithms Domain decomposition Iterative substructuring BDDC Adaptive constraints multilevel algorithms

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Numerical Solution of Markov Chains

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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2011年第6期18卷 897-900页

作者： Benzi, Michele Emory Univ Dept Math & Comp Sci Atlanta GA 30322 USA

This special issue contains a selection of papers from the Sixth International Workshop on the Numerical Solution of Markov Chains, held in Williamsburg, Virginia on September 16-17, 2010. The papers cover a broad range of topics including perturbation theory for absorbing chains, bounding techniques, steady-state and transient solution methods, multilevel algorithms, preconditioning, and applications. Copyright (C) 2011 John Wiley & Sons, Ltd.

关键词： Markov chains multilevel algorithms preconditioning applied probability

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The University of Florida Sparse Matrix Collection

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 2011年第1期38卷 1-1页

作者： Davis, Timothy A. Hu, Yifan Univ Florida CISE Dept Gainesville FL 32610 USA AT&T Labs Res Florham Pk NJ USA

We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications. The Collection is widely used by the numerical linear algebra community for the development and performance evaluation of sparse matrix algorithms. It allows for robust and repeatable experiments: robust because performance results with artificially generated matrices can be misleading, and repeatable because matrices are curated and made publicly available in many formats. Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs). We provide software for accessing and managing the Collection, from MATLAB(TM), Mathematica(TM), Fortran, and C, as well as an online search capability. Graph visualization of the matrices is provided, and a new multilevel coarsening scheme is proposed to facilitate this task.

关键词： algorithms Experimentation Performance Graph drawing performance evaluation multilevel algorithms sparse matrices

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Glimmer: multilevel MDS on the GPU

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2009年第2期15卷 249-261页

作者： Ingram, Stephen Munzne, Tamara Olano, Marc Univ British Columbia Dept Comp Sci Vancouver BC V5Y 1Z6 Canada Univ British Columbia Dept Comp Sci Vancouver BC V6T 1Z4 Canada Univ Maryland Dept Comp Sci & Elect Engn Baltimore MD 21250 USA

We present Glimmer, a new multilevel algorithm for multidimensional scaling designed to exploit modern graphics processing unit (GPU) hardware. We also present GPU-SF, a parallel force-based subsystem used by Glimmer. Glimmer organizes input into a hierarchy of levels and recursively applies GPU-SF to combine and refine the levels. The multilevel nature of the algorithm makes local minima less likely, while the GPU parallelism improves the speed of computation. We propose a robust termination condition for GPU-SF based on a filtered approximation of the normalized stress function. We demonstrate the benefits of Glimmer in terms of speed, normalized stress, and visual quality against several previous algorithms for a range of synthetic and real benchmark data sets. We also show that the performance of Glimmer on GPUs is substantially faster than a CPU implementation of the same algorithm.

关键词： Multidimensional scaling multilevel algorithms optimization GPGPU

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multilevel strategies for parametric shape optimization in aerodynamics

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EUROPEAN JOURNAL OF COMPUTATIONAL MECHANICS 2008年第1-2期17卷 149-168页

作者： Abou El Majd, Badr Desideri, Jean-Antoine Duvigneau, Regis INRIA Opale Project Team 2004 Route LuciolesBP 93 F-06902 Sophia Antipolis France

The essential numerical features of multilevel strategies developed for parametric shape optimization are reviewed. These methods employ nested parameterization supports of either shape, or shape deformation, and the classical process of degree elevation resulting in exact geometrical data transfer from coarse to fine representations. The algorithms mimick classical multigrid strategies and are found very effective in terms of convergence acceleration. In particular, for a drag reduction problem involving a three-dimensional Eulerian transonic flow simulated by an unstructured-grid finite-volume method, the complete algorithm is found to be noticeably superior to the natural algorithm simply based on progressive degree elevation.

关键词： optimum shape design compressible aerodynamics finite-volume methods shape parameterization multilevel algorithms

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On the development of PSBLAS-based parallel two-level Schwarz preconditioners

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APPLIED NUMERICAL MATHEMATICS 2007年第11-12期57卷 1181-1196页

作者： D'Ambra, Pasqua di Serafino, Daniela Filippone, Salvatore Univ Naples 2 Dept Math Via Vivaldi 43 I-81100 Caserta Italy CNR Inst High Performance Comp & Networking I-80131 Naples Italy Univ Roma Tor Vergata Dept Mech Engn Rome Italy

Design and implementation issues that concern the development of a package of parallel algebraic two-level Schwarz preconditioners are discussed. The computations are based on the Parallel Sparse BLAS (PSBLAS) library. The package implements various versions of Additive Schwarz preconditioners and applies a smoothed aggregation technique to generate a coarse-level correction. The coarse matrix can be either replicated on the processors or distributed among them;the corresponding system is solved by factorization or block Jacobi sweeps, respectively. The design of the package started from a description of the preconditioners in terms of parallel basic Linear Algebra operators, in order to develop software based on standard kernels. Suitable preconditioner data structures were defined to fully exploit the existing PSBLAS functionalities;however, the implementation of the preconditioner required also an extension of the set of basic library kernels. The results of experiments carried out on different test matrices show that the package is competitive in terms of runtime efficiency. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： computational kernels parallel software sparse BLAS schwarz preconditioners multilevel algorithms smoothed aggregation

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A two-scale method for radiative heat transfer in non-grey absorbing and emitting media

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JOURNAL OF NUMERICAL MATHEMATICS 2007年第1期15卷 59-79页

作者： Seaid, M. AG Technomath Fachbereich Math D-67663 Kaiserslautern Germany

Multiscale radiative heat transfer (RHT) problems are formulated and methods to approximate their numerical solutions are developed. We focus on RHT problems in participating media with heterogeneous optical properties leading to both optically thick and thin regimes within the same media spectrum. By introducing a diffusive scale and using an asymptotic expansion in the RHT equations we formulate the simplified P-N approximations. The optical spectrum is decomposed in wavelength bands and the RHT equations are solved for bands with low absorption while the simplified P-N equations are solved for bands with high absorption. The hybrid models solve the multiscale RHT more accurately than the simplified PN approximations and with a computational costs less than using the full RHT solver. Accuracy and effectiveness of the proposed models are demonstrated on three-dimensional RHT problems arising in combustion systems.

关键词： radiative heat transfer simplified P-N approximations multiscale problems discrete-ordinate method multilevel algorithms non-grey gases combustion systems

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Parallel and multilevel algorithms for Computational Partial Differential Equations

Parallel and Multilevel Algorithms for Computational Partial...

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2004 International Symposium on Distributed Computing and Applications to Business, Engineering and Science

作者： Peter K Jimack School of Computing University of Leeds

The efficient and reliable solution of partial differential equations(PDEs) plays an essential role in a very large number of applications in business,engineering and science, ranging from the modelling of financial markets through to the prediction of complex fluid *** paper presents a discussion of alternative approaches to the fast solution of elliptic and parabolic PDEs based upon the use of parallel, adaptive and multilevel *** adaptivity is essential to ensure that the solution is approximated to different local resolutions across the domain according to its local properties,whilst the multilevel algorithms ensure that the computational time to solve the resulting finite element equations is proportional to the number of unknowns. Applying these techniques efficiently on parallel computer architectures leads to significant practical problems. Difficulties addressed in this paper include how to handle the coarse grid operations efficiently in parallel and the dynamic load-balancing problem that arises when the finite element mesh is adapted.

关键词： Partial Differential Equations Parallel Computing multilevel algorithms Adaptive Mesh Refinement

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