Multilevel Algorithm for Graph Partitioning - Bochkarev, N. S.; Diyankov, O. V.; Pravilnikov, V. Y. (Matrix Methods: Theory, Algorithms And Applications, 2010)
A class of multilevel algorithms for partitioning of a sparse matrix prior to parallel solution of a system of linear equations is described. This matrix partitioning problem can be described in terms of a graph partitioning problem which is known to be NP-hard, so several heuristics for its solution have been proposed in the past decades. For this purpose we use the multilevel algorithm proposed by B. Hendrickson and R. Leland [2] and further developed by G. Karypis and V. Kumar [3]. This algorithm is very efficient and tends to produce high quality partitioning for a wide range of matrices arising in many practical applications.