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Graph partition

About: Graph partition is a(n) research topic. Over the lifetime, 4324 publication(s) have been published within this topic receiving 159108 citation(s).

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Journal ArticleDOI
Jianbo Shi1, Jitendra Malik2Institutions (2)
TL;DR: This work treats image segmentation as a graph partitioning problem and proposes a novel global criterion, the normalized cut, for segmenting the graph, which measures both the total dissimilarity between the different groups as well as the total similarity within the groups.

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Abstract: We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging.

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13,025 citations


18


Proceedings ArticleDOI
Jianbo Shi1, Jitendra Malik1Institutions (1)
17 Jun 1997-
TL;DR: This work treats image segmentation as a graph partitioning problem and proposes a novel global criterion, the normalized cut, for segmenting the graph, which measures both the total dissimilarity between the different groups as well as the total similarity within the groups.

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Abstract: We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We have applied this approach to segmenting static images and found results very encouraging.

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10,996 citations


18


BookDOI
01 Jan 1999-
TL;DR: This chapter discusses Ant Foraging Behavior, Combinatorial Optimization, and Routing in Communications Networks, and its application to Data Analysis and Graph Partitioning.

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Abstract: 1. Introduction 2. Ant Foraging Behavior, Combinatorial Optimization, and Routing in Communications Networks 3. Division of Labor and Task Allocation 4. Cemetery Organization, Brood Sorting, Data Analysis, and Graph Partitioning 5. Self-Organization and Templates: Application to Data Analysis and Graph Partitioning 6. Nest Building and Self-Assembling 7. Cooperative Transport by Insects and Robots 8. Epilogue

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5,634 citations


Journal ArticleDOI
TL;DR: This work presents a new coarsening heuristic (called heavy-edge heuristic) for which the size of the partition of the coarse graph is within a small factor of theSize of the final partition obtained after multilevel refinement, and presents a much faster variation of the Kernighan--Lin (KL) algorithm for refining during uncoarsening.

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Abstract: Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. of the 6th SIAM Conference on Parallel Processing for Scientific Computing, 1993, 445--452; Hendrickson and Leland, A Multilevel Algorithm for Partitioning Graphs, Tech. report SAND 93-1301, Sandia National Laboratories, Albuquerque, NM, 1993]. From the early work it was clear that multilevel techniques held great promise; however, it was not known if they can be made to consistently produce high quality partitions for graphs arising in a wide range of application domains. We investigate the effectiveness of many different choices for all three phases: coarsening, partition of the coarsest graph, and refinement. In particular, we present a new coarsening heuristic (called heavy-edge heuristic) for which the size of the partition of the coarse graph is within a small factor of the size of the final partition obtained after multilevel refinement. We also present a much faster variation of the Kernighan--Lin (KL) algorithm for refining during uncoarsening. We test our scheme on a large number of graphs arising in various domains including finite element methods, linear programming, VLSI, and transportation. Our experiments show that our scheme produces partitions that are consistently better than those produced by spectral partitioning schemes in substantially smaller time. Also, when our scheme is used to compute fill-reducing orderings for sparse matrices, it produces orderings that have substantially smaller fill than the widely used multiple minimum degree algorithm.

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5,117 citations


12


Journal ArticleDOI
Brian W. Kernighan1, Shou-De LinInstitutions (1)
TL;DR: A heuristic method for partitioning arbitrary graphs which is both effective in finding optimal partitions, and fast enough to be practical in solving large problems is presented.

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Abstract: We consider the problem of partitioning the nodes of a graph with costs on its edges into subsets of given sizes so as to minimize the sum of the costs on all edges cut. This problem arises in several physical situations — for example, in assigning the components of electronic circuits to circuit boards to minimize the number of connections between boards. This paper presents a heuristic method for partitioning arbitrary graphs which is both effective in finding optimal partitions, and fast enough to be practical in solving large problems.

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4,837 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20221
2021183
2020196
2019228
2018202
2017250

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Topic's top 5 most impactful authors

Christian Schulz

57 papers, 1.9K citations

Peter Sanders

37 papers, 1.4K citations

George Karypis

28 papers, 9.8K citations

Henning Meyerhenke

25 papers, 1K citations

Vipin Kumar

18 papers, 9.2K citations