A simple, combinatorial algorithm for solving SDD systems in nearly-linear time
Original manuscript January 28, 2013
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Association for Computing Machinery (ACM)
2013
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| Online Access: | http://hdl.handle.net/1721.1/80391 https://orcid.org/0000-0002-2749-3859 https://orcid.org/0000-0002-4257-4198 |
| _version_ | 1826205250821816320 |
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| author | Orecchia, Lorenzo Zhu, Zeyuan Allen Kelner, Jonathan Adam Sidford, Aaron D. |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Orecchia, Lorenzo Zhu, Zeyuan Allen Kelner, Jonathan Adam Sidford, Aaron D. |
| author_sort | Orecchia, Lorenzo |
| collection | MIT |
| description | Original manuscript January 28, 2013 |
| first_indexed | 2024-09-23T13:09:44Z |
| format | Article |
| id | mit-1721.1/80391 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:09:44Z |
| publishDate | 2013 |
| publisher | Association for Computing Machinery (ACM) |
| record_format | dspace |
| spelling | mit-1721.1/803912022-10-01T13:26:48Z A simple, combinatorial algorithm for solving SDD systems in nearly-linear time Orecchia, Lorenzo Zhu, Zeyuan Allen Kelner, Jonathan Adam Sidford, Aaron D. Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Mathematics Kelner, Jonathan Adam Orecchia, Lorenzo Sidford, Aaron D. Zhu, Zeyuan Allen Original manuscript January 28, 2013 In this paper, we present a simple combinatorial algorithm that solves symmetric diagonally dominant (SDD) linear systems in nearly-linear time. It uses little of the machinery that previously appeared to be necessary for a such an algorithm. It does not require recursive preconditioning, spectral sparsification, or even the Chebyshev Method or Conjugate Gradient. After constructing a "nice" spanning tree of a graph associated with the linear system, the entire algorithm consists of the repeated application of a simple update rule, which it implements using a lightweight data structure. The algorithm is numerically stable and can be implemented without the increased bit-precision required by previous solvers. As such, the algorithm has the fastest known running time under the standard unit-cost RAM model. We hope the simplicity of the algorithm and the insights yielded by its analysis will be useful in both theory and practice. National Science Foundation (U.S.) (Award 0843915) National Science Foundation (U.S.) (Award 1111109) Alfred P. Sloan Foundation (Research Fellowship) National Science Foundation (U.S.). Graduate Research Fellowship Program (Grant 1122374) 2013-09-11T15:37:35Z 2013-09-11T15:37:35Z 2013-06 Article http://purl.org/eprint/type/ConferencePaper 9781450320290 http://hdl.handle.net/1721.1/80391 Jonathan A. Kelner, Lorenzo Orecchia, Aaron Sidford, and Zeyuan Allen Zhu. 2013. A simple, combinatorial algorithm for solving SDD systems in nearly-linear time. In Proceedings of the 45th annual ACM symposium on Symposium on theory of computing (STOC '13). ACM, New York, NY, USA, 911-920. https://orcid.org/0000-0002-2749-3859 https://orcid.org/0000-0002-4257-4198 en_US http://dx.doi.org/10.1145/2488608.2488724 Proceedings of the 45th annual ACM symposium on Symposium on theory of computing (STOC '13) Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Association for Computing Machinery (ACM) arXiv |
| spellingShingle | Orecchia, Lorenzo Zhu, Zeyuan Allen Kelner, Jonathan Adam Sidford, Aaron D. A simple, combinatorial algorithm for solving SDD systems in nearly-linear time |
| title | A simple, combinatorial algorithm for solving SDD systems in nearly-linear time |
| title_full | A simple, combinatorial algorithm for solving SDD systems in nearly-linear time |
| title_fullStr | A simple, combinatorial algorithm for solving SDD systems in nearly-linear time |
| title_full_unstemmed | A simple, combinatorial algorithm for solving SDD systems in nearly-linear time |
| title_short | A simple, combinatorial algorithm for solving SDD systems in nearly-linear time |
| title_sort | simple combinatorial algorithm for solving sdd systems in nearly linear time |
| url | http://hdl.handle.net/1721.1/80391 https://orcid.org/0000-0002-2749-3859 https://orcid.org/0000-0002-4257-4198 |
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