Permuting Sparse Rectangular Matrices into Block-Diagonal Form

Cevdet Aykanat, Ali Pinar, Ümit V. Çatalyürek
2004 SIAM Journal on Scientific Computing  
This work investigates the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for the solution of the deriving problem, which has been recently investigated in the context of mathematical programming, LU factorization and QR factorization. We propose bipartite graph and hypergraph models to represent the nonzero structure of a matrix, which reduce the permutation problem to those of graph partitioning by
more » ... x separator and hypergraph partitioning, respectively. Besides proposing the models to represent sparse matrices and investigating related combinatorial problems, we provide a detailed survey of relevant literature to bridge the gap between di erent societies, investigate existing techniques for partitioning and propose new ones, and nally present a thorough empirical study of these techniques. Our experiments on a wide range of matrices, using state-of-theart graph and hypergraph partitioning tools MeTiS and PaToH, revealed that the proposed methods yield very e ective solutions both in terms of solution quality and runtime.
doi:10.1137/s1064827502401953 fatcat:jeqct56t4jdm5bvmye4xkakv6i