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New Graph Partitioning Algorithms
, 1998
"... Graph partitioning problems are NPcomplete and various heuristic algorithms exist in the litterature. Particularly, spectral graph partitioning algorithms partition the graph using the eigenvector associated with the second smallest eigenvalue of the "graph Laplacian." Through the use of ..."
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Cited by 3 (2 self)
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Graph partitioning problems are NPcomplete and various heuristic algorithms exist in the litterature. Particularly, spectral graph partitioning algorithms partition the graph using the eigenvector associated with the second smallest eigenvalue of the "graph Laplacian." Through the use
Fast Graph Partitioning Algorithms
, 1995
"... In this work, the following kway graph partitioning (GP) problem is considered: given an undirected weighted graph G(V; E), partition the nodes of G into k parts of almost equal size such that the partitioncost (sum of the weights on edges with nodes in different parts) is minimized. Two simple ..."
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Cited by 1 (0 self)
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In this work, the following kway graph partitioning (GP) problem is considered: given an undirected weighted graph G(V; E), partition the nodes of G into k parts of almost equal size such that the partitioncost (sum of the weights on edges with nodes in different parts) is minimized. Two simple
Analysis of Multilevel Graph Partition Algorithm
"... All the recent available graph partitioning packages include the multilevel graph partition algorithm in which the graph is coarsened by a sequence of increasingly smaller graphs. The smallest graph is partitioned using a graph partitioning algorithm and this partition is propagated back through th ..."
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All the recent available graph partitioning packages include the multilevel graph partition algorithm in which the graph is coarsened by a sequence of increasingly smaller graphs. The smallest graph is partitioned using a graph partitioning algorithm and this partition is propagated back through
Engineering Graph Partitioning Algorithms
"... Abstract. The paper gives an overview of our recent work on balanced graph partitioning – partition the nodes of a graph into k blocks such that all blocks have approximately equal size and such that the number of cut edges is small. This problem has numerous applications for example in parallel pro ..."
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Abstract. The paper gives an overview of our recent work on balanced graph partitioning – partition the nodes of a graph into k blocks such that all blocks have approximately equal size and such that the number of cut edges is small. This problem has numerous applications for example in parallel
Randomized Graph Partitioning Algorithms
, 1997
"... In this project, we have studied and worked on results and algorithms centered around (global) minimum cuts in graphs. A cut is a minimal set of edges whose removal from a connected graph disconnects it and a minimum cut is a cut of least capacity. We analyze the combinatorial structure of the set o ..."
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In this project, we have studied and worked on results and algorithms centered around (global) minimum cuts in graphs. A cut is a minimal set of edges whose removal from a connected graph disconnects it and a minimum cut is a cut of least capacity. We analyze the combinatorial structure of the set
Engineering Multilevel Graph Partitioning Algorithms
"... We present a multilevel graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from multigrid linear solvers. Local improvement algorithms are based on maxflow mincut computations and more localized FM searches. By combining these technique ..."
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Cited by 28 (14 self)
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We present a multilevel graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from multigrid linear solvers. Local improvement algorithms are based on maxflow mincut computations and more localized FM searches. By combining
Graph Partitioning Algorithms With Applications To Scientific Computing
 Parallel Numerical Algorithms
, 1997
"... Identifying the parallelism in a problem by partitioning its data and tasks among the processors of a parallel computer is a fundamental issue in parallel computing. This problem can be modeled as a graph partitioning problem in which the vertices of a graph are divided into a specified number of su ..."
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Cited by 50 (0 self)
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of subsets such that few edges join two vertices in different subsets. Several new graph partitioning algorithms have been developed in the past few years, and we survey some of this activity. We describe the terminology associated with graph partitioning, the complexity of computing good separators
Four Cheegertype Inequalities for Graph Partitioning Algorithms ∗
"... We will give proofs to four isoperimetric inequalities which are variations of the original Cheeger inequality relating eigenvalues of a graph with the Cheeger constant. The first is a simplified proof of the classical Cheeger inequality using eigenvectors. The second is based on a rapid mixing resu ..."
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result for random walks by Lovász and Simonovits. The third uses PageRank, a quantitative ranking of the vertices introduced by Brin and Page. The fourth proof is by an improved notion, called the heat kernel pagerank. The four proofs lead to improved graph partitioning algorithms and, in particular
Graph Partitioning Algorithms for Distributing Workloads of Parallel Computations
, 1998
"... This paper surveys graph partitioning algorithms used for parallel computing, with an emphasis on the problem of distributing workloads for parallel computations. Geometric, structural, and refinementbased algorithms are described and contrasted. In addition, multilevel partitioning techniques and ..."
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Cited by 20 (1 self)
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This paper surveys graph partitioning algorithms used for parallel computing, with an emphasis on the problem of distributing workloads for parallel computations. Geometric, structural, and refinementbased algorithms are described and contrasted. In addition, multilevel partitioning techniques
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