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Engineering Data Reduction for Nested Dissection [article]

Wolfgang Ost, Christian Schulz, Darren Strash
2020 arXiv   pre-print
computing orderings with less fill-in.  ...  a node ordering that minimizes the so-called fill-in.  ...  On road networks we obtain orderings with lower fill-in six times faster than nested dissection alone.  ... 
arXiv:2004.11315v1 fatcat:ceirz26xubguff77jzpna52c4a

Improving the Run Time and Quality of Nested Dissection Ordering

Bruce Hendrickson, Edward Rothberg
1998 SIAM Journal on Scientific Computing  
The algorithm is a hybrid of nested dissection and minimum degree ordering, and combines an assortment of different algorithmic advances.  ...  New or improved algorithms are described for graph compression, multilevel partitioning, and separator improvement.  ...  However, once these subgraphs have been ordered, they are eliminated from the graph G and the remaining graph (composed of vertices belonging to the vertex separators found by the nested dissection ordering  ... 
doi:10.1137/s1064827596300656 fatcat:hpv27omhfffutmeelboir6miiu

An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations [article]

Léopold Cambier, Chao Chen, Erik G Boman, Sivasankaran Rajamanickam, Raymond S. Tuminaro, Eric Darve
2020 arXiv   pre-print
It is based on nested dissection, sparsification and low-rank compression.  ...  This operation reduces the size of the separators by eliminating some degrees of freedom but without introducing any fill-in.  ...  Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525. We thank Cindy Orozco for the idea of the modified Nested Dissection algorithm,  ... 
arXiv:1901.02971v3 fatcat:jffakrvs6zbvte2y3htvyyerd4

Customizable Contraction Hierarchies [article]

Julian Dibbelt, Ben Strasser, Dorothea Wagner
2015 arXiv   pre-print
Our Customizable Contraction Hierarchies use nested dissection orders as suggested by Bauer et al.  ...  We provide an in-depth experimental analysis on large road and game maps that clearly shows that Customizable Contraction Hierarchies are a very practicable solution in scenarios where edge weights often  ...  Acknowledgment: We would like to thank Ignaz Rutter and Tim Zeitz for very inspiring conversations.  ... 
arXiv:1402.0402v5 fatcat:cmthoyeeyzavracltsbuxsty7e

Graph Bisection with Pareto-Optimization [article]

Michael Hamann, Ben Strasser
2017 arXiv   pre-print
Using the Pareto-set we can identify cuts with a particularly good trade-off between cut size and balance that can be used to compute contraction and minimum fill-in orders, which can be used in Customizable  ...  Contraction Hierarchies (CCH), a speed-up technique for shortest path computations.  ...  The contraction orders used by CCH, which as based upon nested dissection [25, 36] , are also called minimum fill-in orders in the context of sparse matrices.  ... 
arXiv:1504.03812v3 fatcat:dchyjh3vdvfxrok4w5iot2e7om

Nearest-Neighbor Queries in Customizable Contraction Hierarchies and Applications [article]

Valentin Buchhold, Dorothea Wagner
2021 arXiv   pre-print
Customizable contraction hierarchies are one of the most popular route planning frameworks in practice, due to their simplicity and versatility.  ...  In this work, we present a novel algorithm for finding k-nearest neighbors in customizable contraction hierarchies by systematically exploring the associated separator decomposition tree.  ...  The preprocessing phase computes a separator decomposition of G, determines an associated nested dissection order on the vertices in G, and contracts them in this order.  ... 
arXiv:2103.10359v1 fatcat:vi5wedbk6rftvcaxmkqe3htc5m

Computing Tree Decompositions with FlowCutter: PACE 2017 Submission [article]

Ben Strasser
2017 arXiv   pre-print
The algorithm was originally developed in the context of accelerating shortest path computation on road graphs using multilevel partitions.  ...  It was the only competitor to solve all instances and won a tight second place.  ...  It made the experimental evaluation easier and less error-prone. I thank Michael Hamann for fruitful discussions.  ... 
arXiv:1709.08949v1 fatcat:gl7wrbv3gfbbjfiotiqkr3f7fy

A survey of direct methods for sparse linear systems

Timothy A. Davis, Sivasankaran Rajamanickam, Wissam M. Sid-Lakhdar
2016 Acta Numerica  
A glimpse of the breadth of applications relying on sparse solvers can be seen in the origins of matrices in published matrix benchmark collections (Duff and Reid 1979a , Duff, Grimes and Lewis 1989a ,  ...  They exploit the sparsity of a matrix to solve problems economically: much faster and using far less memory than if all the entries of a matrix were stored and took part in explicit computations.  ...  Department of Energy under contract DE-AC04-94-AL85000.  ... 
doi:10.1017/s0962492916000076 fatcat:u4dqyjkjqnelll5e3ywm7lqkca

Faster Customization of Road Networks [chapter]

Daniel Delling, Renato F. Werneck
2013 Lecture Notes in Computer Science  
A wide variety of algorithms can answer exact shortest-path queries in real time on continental road networks, but they typically require significant preprocessing effort.  ...  We reduce customization time even further, by an order of magnitude. This makes it worthwhile even when a single query is to be run, enabling a host of new applications.  ...  Vetter for making his code [19] available, and T. Pajor for running it.  ... 
doi:10.1007/978-3-642-38527-8_5 fatcat:lp4hlwrri5fshfzgfiymekmuai

Helmert's and Bowie's geodetic mapping methods and their relation to graph-based SLAM

Pratik Agarwal, Wolfram Burgard, Cyrill Stachniss
2014 2014 IEEE International Conference on Robotics and Automation (ICRA)  
In this paper, we explain two key geodetic mapping methods that we believe are relevant for robotics.  ...  build maps and use them for navigation.  ...  This work has been partially supported by BMBF under contract number 13EZ1129B-iView, by the MWK for the project ZAFL-AAL and by the EC under contract numbers ERG-AG-PE7-267686-LifeNav and FP7-600890-ROVINA  ... 
doi:10.1109/icra.2014.6907382 dblp:conf/icra/AgarwalBS14 fatcat:wh22viinhneelop4rcoe2cetma

Recursive Approach in Sparse Matrix LU Factorization

Jack Dongarra, Victor Eijkhout, Piotr Łuszczek
2001 Scientific Programming  
Performance results given here show that the recursive approach may perform comparable to leading software packages for sparse matrix factorization in terms of execution time, memory usage, and error estimates  ...  The recursive formulation of common linear algebra codes has been proven very successful in dense matrix computations. An extension of the recursive technique for sparse matrices is presented.  ...  ; and by the University of California Berkeley through subcontract number SA1248PG, as part of the prime contract DEFG03-94ER25219 from the Department of Energy.  ... 
doi:10.1155/2001/569670 fatcat:ar55cwn3hjddtc3l3a3qjd6nce

Recent Advances in Practical Data Reduction [article]

Faisal Abu-Khzam, Sebastian Lamm, Matthias Mnich, Alexander Noe, Christian Schulz, Darren Strash
2020 arXiv   pre-print
Over the last two decades, significant advances have been made in the design and analysis of fixed-parameter algorithms for a wide variety of graph-theoretic problems.  ...  Moreover, we describe concrete techniques that may be useful for future implementations in the area and give open problems and research questions.  ...  Partially supported by DFG grants MN 59/1-1 and SCHU 2567/1-2.  ... 
arXiv:2012.12594v3 fatcat:vpsucno5cvgotovfiihkyyytba

Graph Sketching Against Adaptive Adversaries Applied to the Minimum Degree Algorithm [article]

Matthew Fahrbach, Gary L. Miller, Richard Peng, Saurabh Sawlani, Junxing Wang, Shen Chen Xu
2018 arXiv   pre-print
fill degrees of a matrix undergoing elimination in O(polylog(n)) time per elimination and query.  ...  Motivated by the study of matrix elimination orderings in combinatorial scientific computing, we utilize graph sketching and local sampling to give a data structure that provides access to approximate  ...  Acknowledgements We thank John Gilbert and Gramoz Goranci for many helpful discussions regarding various topics in this paper.  ... 
arXiv:1804.04239v1 fatcat:v5ntwspqnjeqvofsfjho4dwp7m

Recent advances in sparse linear solver technology for semiconductor device simulation matrices

O. Schenk, M. Hagemann, S. Rollin
2003 International Conference on Simulation of Semiconductor Processes and Devices, 2003. SISPAD 2003.  
In this paper, it is shown that nonsymmetric permutations and scalings aimed at placing large entries on the diagonal greatly enhance the reliability of direct and iterative methods.  ...  This paper discusses recent advances in the development of robust direct and iterative sparse linear solvers for general unsymmetric linear systems of equations.  ...  SuperLU dist uses the multiple minimum degree, WSMP and PARDISO use a nested dissection ordering, and UMFPACK uses a column approximate minimum degree algorithm to compute a fill-in reducing reordering  ... 
doi:10.1109/sispad.2003.1233648 fatcat:bevsymsdubcsrmtgeqk5r2mgse

Scalable Graph Algorithms [article]

Christian Schulz
2019 arXiv   pre-print
In order to find these patterns, massive amounts of data have to be acquired and processed.  ...  Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain.  ...  While the grants are acknowledged in the individual papers, we also acknowledge them here.  ... 
arXiv:1912.00245v1 fatcat:mop2e6pqtnbr7irkrakraael6a
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