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16
Multilevel algorithms for linear ordering problems
, 2007
"... Linear ordering problems are combinatorial optimization problems which deal with the minimization of different functionals in which the graph vertices are mapped onto (1, 2,..., n). These problems are widely used and studied in many practical and theoretical applications. In this paper we present a ..."
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Cited by 10 (6 self)
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Linear ordering problems are combinatorial optimization problems which deal with the minimization of different functionals in which the graph vertices are mapped onto (1, 2,..., n). These problems are widely used and studied in many practical and theoretical applications. In this paper we present a variety of lineartime algorithms for these problems inspired by the Algebraic Multigrid approach which is based on weighted edge contraction. The experimental result for four such problems turned out to be better than every known result in almost all cases, while the short running time of the algorithms enables testing very large graphs.
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 (3 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.
Comparison of coarsening schemes for multilevel graph partitioning
 in: Learning and Intelligent Optimization: Third International Conference, LION 3. Selected Papers
, 2009
"... partitioning ..."
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 5 (3 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.
Memetic algorithms for the MinLA problem
 Lecture Notes in Computer Science
"... Abstract. This paper presents a new Memetic Algorithm designed to compute near optimal solutions for the MinLA problem. It incorporates a highly specialized crossover operator, a fast MinLA heuristic used to create the initial population and a local search operator based on a fine tuned Simulated An ..."
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Cited by 2 (1 self)
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Abstract. This paper presents a new Memetic Algorithm designed to compute near optimal solutions for the MinLA problem. It incorporates a highly specialized crossover operator, a fast MinLA heuristic used to create the initial population and a local search operator based on a fine tuned Simulated Annealing algorithm. Its performance is investigated through extensive experimentation over well known benchmarks andcomparedwithotherstateoftheartalgorithms. Key words: Memetic Algorithms, Linear Arrangement, Heuristics. 1
Fast Multilevel Clustering
"... Clustering is a difficult problem. Clustering data may differ by a variety of aspects (dimensionality, cluster size, noise, etc), and the criterion for clustering may depend on the context in which the data is given. We present a multilevel approach for clustering, easily adaptable to handle various ..."
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Cited by 2 (1 self)
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Clustering is a difficult problem. Clustering data may differ by a variety of aspects (dimensionality, cluster size, noise, etc), and the criterion for clustering may depend on the context in which the data is given. We present a multilevel approach for clustering, easily adaptable to handle various kinds of data by identifying desired underlying features of the data. The scheme we present is given a similarity graph, on which we apply a recursive coarsening process, resulting in a pyramid of graphs in time that is linear in the number of edges in the graph. The pyramid provides a hierarchal decomposition of the data into clusters in all resolutions, and data points are associated to clusters with soft relations. We demonstrate the algorithm by applying it successfully to challenging clustering problems.
A refined evaluation function for the MinLA problem
 Lecture Notes in Computer Science
, 2006
"... Abstract. This paper introduces a refined evaluation function, called Φ, for the Minimum Linear Arrangement problem (MinLA). Compared with the classical evaluation function (LA), Φ integrates additional information contained in an arrangement to distinguish arrangements with the same LA value. The m ..."
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Cited by 1 (0 self)
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Abstract. This paper introduces a refined evaluation function, called Φ, for the Minimum Linear Arrangement problem (MinLA). Compared with the classical evaluation function (LA), Φ integrates additional information contained in an arrangement to distinguish arrangements with the same LA value. The main characteristics of Φ are analyzed and its practical usefulness is assessed within both a Steepest Descent (SD) algorithm and a Memetic Algorithm (MA). Experiments show that the use of Φ allows to boost the performance of SD and MA, leading to the improvement on some previous best known solutions.
Improving Random Walk Performance
"... Abstract — 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 o ..."
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Cited by 1 (0 self)
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Abstract — 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
J.T.: A Continuous Quadratic Programming Formulation of the Vertex Separator Problem
"... Abstract. The Vertex Separator Problem (VSP) for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets of roughly equal size. In a recent paper (Optimality Conditions For Maximizing a Function Over a Polyhedron, Mathematical Programming, ..."
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Abstract. The Vertex Separator Problem (VSP) for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets of roughly equal size. In a recent paper (Optimality Conditions For Maximizing a Function Over a Polyhedron, Mathematical Programming, 2013, doi: 10.1007/s1010701306441), the authors announced a new continuous bilinear quadratic programming formulation of the VSP, and they used this quadratic programming problem to illustrate the new optimality conditions. The current paper develops conditions for the equivalence between this continuous quadratic program and the vertex separator problem, and it examines the relationship between the continuous formulation of the VSP and continuous quadratic programming formulations for both the edge separator problem and maximum clique problem.