| dc.contributor.author | Cifuentes, Diego Fernando | |
| dc.contributor.author | Parrilo, Pablo A | |
| dc.date.accessioned | 2018-04-23T17:01:52Z | |
| dc.date.available | 2018-04-23T17:01:52Z | |
| dc.date.issued | 2015-12 | |
| dc.date.submitted | 2015-08 | |
| dc.identifier.issn | 0024-3795 | |
| dc.identifier.uri | http://hdl.handle.net/1721.1/114872 | |
| dc.description.abstract | We present an efficient algorithm to compute permanents, mixed discriminants and hyperdeterminants of structured matrices and multidimensional arrays (tensors). We describe the sparsity structure of an array in terms of a graph, and we assume that its treewidth, denoted as ω, is small. Our algorithm requires Õ(n2[superscript ω]) arithmetic operations to compute permanents, and Õ(n[superscript 2] + n3[superscript ω]) for mixed discriminants and hyperdeterminants. We finally show that mixed volume computation continues to be hard under bounded treewidth assumptions. Keywords: Permanent; Structured array; Mixed discriminant;
Treewidth; Hyperdeterminant | en_US |
| dc.description.sponsorship | United States. Air Force Office of Scientific Research (Grant FA9550-11-1-0305) | en_US |
| dc.publisher | Elsevier | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1016/J.LAA.2015.12.004 | en_US |
| dc.rights | Creative Commons Attribution-NonCommercial-NoDerivs License | en_US |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | en_US |
| dc.source | arXiv | en_US |
| dc.title | An efficient tree decomposition method for permanents and mixed discriminants | en_US |
| dc.type | Article | en_US |
| dc.identifier.citation | Cifuentes, Diego, and Pablo A. Parrilo. “An Efficient Tree Decomposition Method for Permanents and Mixed Discriminants.” Linear Algebra and Its Applications 493 (March 2016): 45–81 © 2015 Elsevier | 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 | Linear Algebra and its Applications | en_US |
| dc.eprint.version | Original manuscript | en_US |
| dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
| eprint.status | http://purl.org/eprint/status/NonPeerReviewed | en_US |
| dc.date.updated | 2018-04-19T19:39:47Z | |
| 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_CC | en_US |
