Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
Finding good approximate vertex and edge partitions is NP-hard
Information Processing Letters
A linear-time heuristic for improving network partitions
DAC '82 Proceedings of the 19th Design Automation Conference
Multilevel algorithms for linear ordering problems
Journal of Experimental Algorithmics (JEA)
Comparison of Coarsening Schemes for Multilevel Graph Partitioning
Learning and Intelligent Optimization
Engineering algorithms for approximate weighted matching
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Engineering multilevel graph partitioning algorithms
ESA'11 Proceedings of the 19th European conference on Algorithms
SIAM Journal on Scientific Computing
Engineering graph partitioning algorithms
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
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The graph partitioning problem is widely used and studied in many practical and theoretical applications. Today multilevel strategies represent one of the most effective and efficient generic frameworks for solving this problem on large-scale graphs. Most of the attention in designing 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 AMG-based 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.