I. Safro, P. Sanders, C. Schulz, "Advanced Coarsening Schemes for Graph Partitioning," Experimental Algorithms, Lecture Notes in Computer Science, vol. 7276, Bordeaux, France, Springer-Verlag, 2012, pp. 369-380. Also Preprint ANL/MCS-P2016-0112, January 2012. [pdf]
The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most eeffective and efficient generic frameworks for solving this problem on large-scale graphs. Most of the attention in designing the 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.