Reducing elimination tree height for parallel LU factorization of sparse unsymmetric matrices

• Published in: 2014 21st International Conference on High Performance Computing (HiPC) pp. 1 - 10
• Main Authors: Kayaaslan, Enver, Ucar, Bora
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2014
• Subjects: critical path scheduling; elimination tree; Matrix decomposition; Parallel processing; Particle separators; sparse LU factorization; Sparse matrices; Symmetric matrices; unsymmetric matrices; Vegetation
• ISSN: 1094-7256; 2640-0316
• DOI: 10.1109/HiPC.2014.7116880

The elimination tree for unsymmetric matrices is a recent model playing important roles in sparse LU factorization. This tree captures the dependencies between the tasks of some well-known variants of sparse LU factorization. Therefore, the height of the elimination tree corresponds to the critical path length of the task dependency graph in the corresponding parallel LU factorization methods. We investigate the problem of finding minimum height elimination trees to expose a maximum degree of parallelism by minimizing the critical path length. This problem has recently been shown to be NP-complete. Therefore, we propose heuristics, which generalize the most successful approaches used for symmetric matrices to unsymmetric ones. We test the proposed heuristics on a large set of real world matrices and report 28% reduction in the elimination tree heights with respect to a common method, which exploits the state of the art tools used in Cholesky factorization.