An efficient tree decomposition method for permanents and mixed discriminants
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Parrilo_An efficient.pdf
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Author(s)
Cifuentes, Diego Fernando
Parrilo, Pablo A
Date Issued
December 2015
Journal
Linear Algebra and its Applications
Publisher
Elsevier
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
Version
Original manuscript
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
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.LAA.2015.12.004
