Results 11  20
of
387
Comparing community structure identification
 Journal of Statistical Mechanics: Theory and Experiment
, 2005
"... ..."
PLTMG: A Software Package for Solving Elliptic Partial Differential Equations. Users
 Guide 6.0, Society for Industrial and Applied Mathematics
, 1990
"... Copyright (c) 2004, by the author. ..."
Spectral Partitioning Works: Planar graphs and finite element meshes
 In IEEE Symposium on Foundations of Computer Science
, 1996
"... Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extr ..."
Abstract

Cited by 144 (8 self)
 Add to MetaCart
Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on boundeddegree planar graphs and finite element meshes the classes of graphs to which they are usually applied. While naive spectral bisection does not necessarily work, we prove that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is O( p n) for boundeddegree planar graphs and twodimensional meshes and O i n 1=d j for wellshaped ddimensional meshes. The heart of our analysis is an upper bound on the secondsmallest eigenvalues of the Laplacian matrices of these graphs. 1. Introduction Spectral partitioning has become one of the mos...
Communication Optimizations for Irregular Scientific Computations on Distributed Memory Architectures
 Journal of Parallel and Distributed Computing
, 1993
"... This paper describes a number of optimizations that can be used to support the efficient execution of irregular problems on distributed memory parallel machines. These primitives (1) coordinate interprocessor data movement, (2) manage the storage of, and access to, copies of offprocessor data, (3) ..."
Abstract

Cited by 138 (17 self)
 Add to MetaCart
This paper describes a number of optimizations that can be used to support the efficient execution of irregular problems on distributed memory parallel machines. These primitives (1) coordinate interprocessor data movement, (2) manage the storage of, and access to, copies of offprocessor data, (3) minimize interprocessor communication requirements and (4) support a shared name space. We present a detailed performance and scalability analysis of the communication primitives. This performance and scalability analysis is carried out using a workload generator, kernels from real applications and a large unstructured adaptive application (the molecular dynamics code CHARMM). 1 Introduction Over the past few years we have developed a methodology to produce efficient distributed memory code for sparse and unstructured problems in which array accesses are made through a level of indirection. In such problems the dependency structure is determined by variable values known only at runtime. In...
METIS  Unstructured Graph Partitioning and Sparse Matrix Ordering System, Version 2.0
, 1995
"... this paper is organized as follows: Section 2 briefly describes the various ideas and algorithms implemented in METIS. Section 3 describes the user interface to the METIS graph partitioning and sparse matrix ordering packages. Sections 4 and 5 describe the formats of the input and output files used ..."
Abstract

Cited by 122 (5 self)
 Add to MetaCart
this paper is organized as follows: Section 2 briefly describes the various ideas and algorithms implemented in METIS. Section 3 describes the user interface to the METIS graph partitioning and sparse matrix ordering packages. Sections 4 and 5 describe the formats of the input and output files used by METIS. Section 6 describes the standalone library that implements the various algorithms implemented in METIS. Section 7 describes the system requirements for the METIS package. Appendix A describes and compares various graph partitioning algorithms that are extensively used.
Highly scalable parallel algorithms for sparse matrix factorization
 IEEE Transactions on Parallel and Distributed Systems
, 1994
"... In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our algo ..."
Abstract

Cited by 116 (29 self)
 Add to MetaCart
In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our algorithm substantially improves the state of the art in parallel direct solution of sparse linear systems—both in terms of scalability and overall performance. It is a well known fact that dense matrix factorization scales well and can be implemented efficiently on parallel computers. In this paper, we present the first algorithm to factor a wide class of sparse matrices (including those arising from two and threedimensional finite element problems) that is asymptotically as scalable as dense matrix factorization algorithms on a variety of parallel architectures. Our algorithm incurs less communication overhead and is more scalable than any previously known parallel formulation of sparse matrix factorization. Although, in this paper, we discuss Cholesky factorization of symmetric positive definite matrices, the algorithms can be adapted for solving sparse linear least squares problems and for Gaussian elimination of diagonally dominant matrices that are almost symmetric in structure. An implementation of our sparse Cholesky factorization algorithm delivers up to 20 GFlops on a Cray T3D for mediumsize structural engineering and linear programming problems. To the best of our knowledge,
Randomwalk computation of similarities between nodes of a graph, with application to collaborative recommendation
 IEEE Transactions on Knowledge and Data Engineering
, 2006
"... Abstract—This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted and undirected graph. It is based on a Markovchain model of random walk through the database. More precisely, we compute quantities (the average comm ..."
Abstract

Cited by 116 (14 self)
 Add to MetaCart
Abstract—This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted and undirected graph. It is based on a Markovchain model of random walk through the database. More precisely, we compute quantities (the average commute time, the pseudoinverse of the Laplacian matrix of the graph, etc.) that provide similarities between any pair of nodes, having the nice property of increasing when the number of paths connecting those elements increases and when the “length ” of paths decreases. It turns out that the square root of the average commute time is a Euclidean distance and that the pseudoinverse of the Laplacian matrix is a kernel matrix (its elements are inner products closely related to commute times). A principal component analysis (PCA) of the graph is introduced for computing the subspace projection of the node vectors in a manner that preserves as much variance as possible in terms of the Euclidean commutetime distance. This graph PCA provides a nice interpretation to the “Fiedler vector, ” widely used for graph partitioning. The model is evaluated on a collaborativerecommendation task where suggestions are made about which movies people should watch based upon what they watched in the past. Experimental results on the MovieLens database show that the Laplacianbased similarities perform well in comparison with other methods. The model, which nicely fits into the socalled “statistical relational learning ” framework, could also be used to compute document or word similarities, and, more generally, it could be applied to machinelearning and patternrecognition tasks involving a relational database. Index Terms—Graph analysis, graph and database mining, collaborative recommendation, graph kernels, spectral clustering, Fiedler vector, proximity measures, statistical relational learning. 1
Geometric Mesh Partitioning: Implementation and Experiments
"... We investigate a method of dividing an irregular mesh into equalsized pieces with few interconnecting edges. The method’s novel feature is that it exploits the geometric coordinates of the mesh vertices. It is based on theoretical work of Miller, Teng, Thurston, and Vavasis, who showed that certain ..."
Abstract

Cited by 102 (19 self)
 Add to MetaCart
We investigate a method of dividing an irregular mesh into equalsized pieces with few interconnecting edges. The method’s novel feature is that it exploits the geometric coordinates of the mesh vertices. It is based on theoretical work of Miller, Teng, Thurston, and Vavasis, who showed that certain classes of “wellshaped” finite element meshes have good separators. The geometric method is quite simple to implement: we describe a Matlab code for it in some detail. The method is also quite efficient and effective: we compare it with some other methods, including spectral bisection.
Automated Tag Clustering: Improving search and exploration in the tag space
 In Proc. of the Collaborative Web Tagging Workshop at WWW’06
, 2006
"... In this paper we discuss the use of clustering techniques to enhance the user experience and thus the success of collaborative tagging services. We show that clustering techniques can improve the user experience of current tagging services. ..."
Abstract

Cited by 100 (0 self)
 Add to MetaCart
In this paper we discuss the use of clustering techniques to enhance the user experience and thus the success of collaborative tagging services. We show that clustering techniques can improve the user experience of current tagging services.
Computing communities in large networks using random walks
 J. of Graph Alg. and App. bf
, 2004
"... Dense subgraphs of sparse graphs (communities), which appear in most realworld complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advan ..."
Abstract

Cited by 94 (2 self)
 Add to MetaCart
Dense subgraphs of sparse graphs (communities), which appear in most realworld complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm, called Walktrap, which runs in time O(mn 2) and space O(n 2) in the worst case, and in time O(n 2 log n) and space O(n 2) in most realworld cases (n and m are respectively the number of vertices and edges in the input graph). Extensive comparison tests show that our algorithm surpasses previously proposed ones concerning the quality of the obtained community structures and that it stands among the best ones concerning the running time.