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RELAXATIONBASED COARSENING AND MULTISCALE GRAPH ORGANIZATION
"... In this paper we generalize and improve the multiscale organization of graphs by introducing a new measure that quantifies the “closeness” between two nodes. The calculation of the measure is linear in the number of edges in the graph and involves just a small number of relaxation sweeps. A similar ..."
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Cited by 14 (8 self)
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In this paper we generalize and improve the multiscale organization of graphs by introducing a new measure that quantifies the “closeness” between two nodes. The calculation of the measure is linear in the number of edges in the graph and involves just a small number of relaxation sweeps. A similar notion of distance is then calculated and used at each coarser level. We demonstrate the use of this measure in multiscale methods for several important combinatorial optimization problems and discuss the multiscale graph organization.
Comparison of coarsening schemes for multilevel graph partitioning
 in: Learning and Intelligent Optimization: Third International Conference, LION 3. Selected Papers
, 2009
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Advanced Coarsening Schemes for Graph Partitioning
 IN PROCEEDINGS OF THE 11TH INTERNATIONAL SYMPOSIUM ON EXPERIMENTAL ALGORITHMS (SEA’12), SER. LNCS
, 2012
"... The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on largescale graphs. Most of the attention in designing the multi ..."
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Cited by 9 (7 self)
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The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on largescale graphs. Most of the attention in designing the multilevel partitioning frameworks has been on the refinement phase. In this work we focus on the coarsening phase, which is responsible for creating structurally similar to the original but smaller graphs. We compare different matching and AMGbased coarsening schemes, experiment with the algebraic distance between nodes, and demonstrate computational results on several classes of graphs that emphasize the running time and quality advantages of different coarsenings.
A Multilevel Algorithm for the Minimum 2sum Problem
"... In this paper we introduce a direct motivation for solving the minimum 2sum problem, for which we present a lineartime algorithm inspired by the Algebraic Multigrid approach which is based on weighted edge contraction. Our results turned out to be better than previous results, while the short runn ..."
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Cited by 6 (4 self)
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In this paper we introduce a direct motivation for solving the minimum 2sum problem, for which we present a lineartime algorithm inspired by the Algebraic Multigrid approach which is based on weighted edge contraction. Our results turned out to be better than previous results, while the short running time of the algorithm enabled experiments with very large graphs. We thus introduce a new benchmark for the minimum 2sum problem which contains 66 graphs of various characteristics. In addition, we propose the straightforward use of a part of our algorithm as a powerful local reordering method for any other (than multilevel) framework.
Improving Random Walk Performance
"... Random walk simulation is employed in many experimental algorithmic applications. Efficient execution on modern computer architectures demands that the random walk be implemented to exploit data locality for improving the cache performance. In this research, we demonstrate how different onedimens ..."
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Cited by 2 (0 self)
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Random walk simulation is employed in many experimental algorithmic applications. Efficient execution on modern computer architectures demands that the random walk be implemented to exploit data locality for improving the cache performance. In this research, we demonstrate how different onedimensional data reordering functionals can be used as a preprocessing step for speeding the random walk runtime.
HYPERGRAPHBASED COMBINATORIAL OPTIMIZATION OF MATRIXVECTOR MULTIPLICATION
, 2009
"... Combinatorial scientific computing plays an important enabling role in computational science, particularly in high performance scientific computing. In this thesis, we will describe our work on optimizing matrixvector multiplication using combinatorial techniques. Our research has focused on two di ..."
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Combinatorial scientific computing plays an important enabling role in computational science, particularly in high performance scientific computing. In this thesis, we will describe our work on optimizing matrixvector multiplication using combinatorial techniques. Our research has focused on two different problems in combinatorial scientific computing, both involving matrixvector multiplication, and both are solved using hypergraph models. For both of these problems, the cost of the combinatorial optimization process can be effectively amortized over many matrixvector products. The first problem we address is optimization of serial matrixvector multiplication for relatively small, dense matrices that arise in finite element assembly. Previous work showed that combinatorial optimization of matrixvector multiplication can lead to faster assembly of finite element stiffness matrices by eliminating redundant operations. Based on a graph model characterizing row relationships, a more efficient set of operations can be generated to perform matrixvector multiplication. We improved this graph model by extending the
Algorithms for Visualizing Large Networks
, 2010
"... Graphs are often used to encapsulate relationship between objects. Graph drawing enables visualization of such relationships. The usefulness of this visual representation is dependent on whether the drawing is aesthetic. While there are no strict criteria for aesthetics of a drawing, it is generally ..."
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Graphs are often used to encapsulate relationship between objects. Graph drawing enables visualization of such relationships. The usefulness of this visual representation is dependent on whether the drawing is aesthetic. While there are no strict criteria for aesthetics of a drawing, it is generally agreed, for example,
Advances in Parallel Partitioning, Load Balancing and Matrix Ordering for Scientific Computing
"... Abstract. We summarize recent advances in partitioning, load balancing, and matrix ordering for scientific computing performed by members of the CSCAPES SciDAC institute. 1. ..."
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Abstract. We summarize recent advances in partitioning, load balancing, and matrix ordering for scientific computing performed by members of the CSCAPES SciDAC institute. 1.
A FAST MULTIGRID ALGORITHM FOR ENERGY MINIMIZATION UNDER PLANAR DENSITY CONSTRAINTS
"... Abstract. The twodimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or inequality density constraints, we present a linear t ..."
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Abstract. The twodimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or inequality density constraints, we present a linear time multigrid algorithm for solving correction to this problem. The method is demonstrated on various graph drawing (visualization) instances.
Multilevel algorithms for combinatorial optimization problems Published papers format Advisors
"... The Multiscale method is a class of algorithmic techniques for solving efficiently and effectively largescale computational and optimization problems. This method was originally invented for solving elliptic partial differential equations and up to now it represents the most effective class of nume ..."
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The Multiscale method is a class of algorithmic techniques for solving efficiently and effectively largescale computational and optimization problems. This method was originally invented for solving elliptic partial differential equations and up to now it represents the most effective class of numerical algorithms for them. During the last two decades, there were many successful attempts to adapt the multiscale method for combinatorial optimization problems. Whereas the variety of continuous systems’ multiscale algorithms turned into a separate field of applied mathematics, for combinatorial optimization problems they still have not reached an advanced stage of development, consisting in practice of a very limited number of multiscale techniques. The main goal of this dissertation is to extend the knowledge of multiscale techniques for the combinatorial optimization problems. In the first part of this dissertation we formulate the principles of designing the multilevel algorithms for combinatorial optimization problems defined on a simple graph (or matrix) model. We present the results for a variety of linear ordering