dc.contributor.author | Cifuentes, Diego Fernando | |
dc.contributor.author | Parrilo, Pablo A | |
dc.date.accessioned | 2017-03-27T13:53:33Z | |
dc.date.available | 2017-03-27T13:53:33Z | |
dc.date.issued | 2016-08 | |
dc.date.submitted | 2016-05 | |
dc.identifier.issn | 0895-4801 | |
dc.identifier.issn | 1095-7146 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/107708 | |
dc.description.abstract | Chordal structure and bounded treewidth allow for efficient computation in numerical linear algebra, graphical models, constraint satisfaction, and many other areas. In this paper, we begin the study of how to exploit chordal structure in computational algebraic geometry---in particular, for solving polynomial systems. The structure of a system of polynomial equations can be described in terms of a graph. By carefully exploiting the properties of this graph (in particular, its chordal completions), more efficient algorithms can be developed. To this end, we develop a new technique, which we refer to as chordal elimination, that relies on elimination theory and Gröbner bases. By maintaining graph structure throughout the process, chordal elimination can outperform standard Gröbner bases algorithms in many cases. The reason is because all computations are done on “smaller” rings of size equal to the treewidth of the graph (instead of the total number of variables). In particular, for a restricted class of ideals, the computational complexity is linear in the number of variables. Chordal structure arises in many relevant applications. We demonstrate the suitability of our methods in examples from graph colorings, cryptography, sensor localization, and differential equations. | en_US |
dc.description.sponsorship | United States. Air Force Office of Scientific Research (grant FA9550-11-1-0305) | en_US |
dc.language.iso | en_US | |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1137/151002666 | en_US |
dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
dc.source | SIAM | en_US |
dc.title | Exploiting Chordal Structure in Polynomial Ideals: A Gröbner Bases Approach | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Cifuentes, Diego, and Pablo A. Parrilo. "Exploiting Chordal Structure in Polynomial Ideals: A Gröbner Bases Approach." SIAM Journal on Discrete Mathematics 30.3 (2016): 1534-570. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science | en_US |
dc.contributor.mitauthor | Cifuentes, Diego Fernando | |
dc.contributor.mitauthor | Parrilo, Pablo A | |
dc.relation.journal | SIAM Journal on Discrete Mathematics | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Cifuentes, Diego; Parrilo, Pablo A. | en_US |
dspace.embargo.terms | N | en_US |
dc.identifier.orcid | https://orcid.org/0000-0003-0222-3761 | |
dc.identifier.orcid | https://orcid.org/0000-0003-1132-8477 | |
mit.license | PUBLISHER_POLICY | en_US |