Constructing Elimination Trees for Sparse Unsymmetric Matrices

Kaya, Kamer; Uçar, Bora

doi:10.1137/110825443

Cited by 2 publications

(2 citation statements)

References 13 publications

(19 reference statements)

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“…Currently the algorithm with the best worst-case time complexity has a running time of O(m log n) [26]-another algorithm with the worst-case time complexity of O(mn) [16] performs well in practice as well.…”

Section: Basicsmentioning

confidence: 99%

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

Kayaaslan

Uçar

2014

2014 21st International Conference on High Performance Computing (HiPC)

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To cite this version:Enver Kayaaslan, Bora Uçar. Reducing elimination tree height for parallel LU factorization of sparse unsymmetric matrices.Abstract-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.

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Section: Basicsmentioning

confidence: 99%

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

Kayaaslan

Uçar

2014

2014 21st International Conference on High Performance Computing (HiPC)

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“…We denote the treedepth of a graph G by td(G). The vertex ranking number finds applications in sparse matrix factorization [13,18,20] and VLSI layout problems [19]. This notion also has important connections to the structure of sparse graphs.…”

Section: Introductionmentioning

confidence: 99%

A Faster Parameterized Algorithm for Treedepth

Reidl

Rossmanith

Villaamil

et al. 2014

Lecture Notes in Computer Science

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The width measure treedepth, also known as vertex ranking, centered coloring and elimination tree height, is a well-established notion which has recently seen a resurgence of interest. We present an algorithm which-given as input an n-vertex graph, a tree decomposition of the graph of width w, and an integer t-decides Treedepth, i.e. whether the treedepth of the graph is at most t, in time 2 O(wt) · n. If necessary, a witness structure for the treedepth can be constructed in the same running time. In conjunction with previous results we provide a simple algorithm and a fast algorithm which decide treedepth in time 2 2 O(t) · n and 2 O(t 2 ) · n, respectively, which do not require a tree decomposition as part of their input. The former answers an open question posed by Ossona de Mendez and Nešetřil as to whether deciding Treedepth admits an algorithm with a linear running time (for every fixed t) that does not rely on Courcelle's Theorem or other heavy machinery. For chordal graphs we can prove a running time of 2 O(t log t) · n for the same algorithm. * Research funded by DFG-Project RO 927/13-1 "Pragmatic Parameterized Algorithms".

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Constructing Elimination Trees for Sparse Unsymmetric Matrices

Cited by 2 publications

References 13 publications

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

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

A Faster Parameterized Algorithm for Treedepth

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