License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.52
URN: urn:nbn:de:0030-drops-124590
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12459/
Fürer, Martin ;
Hoppen, Carlos ;
Trevisan, Vilmar
Efficient Diagonalization of Symmetric Matrices Associated with Graphs of Small Treewidth
Abstract
Let M = (m_{ij}) be a symmetric matrix of order n and let G be the graph with vertex set {1,…,n} such that distinct vertices i and j are adjacent if and only if m_{ij} ≠ 0. We introduce a dynamic programming algorithm that finds a diagonal matrix that is congruent to M. If G is given with a tree decomposition ? of width k, then this can be done in time O(k|?| + k² n), where |?| denotes the number of nodes in ?.
BibTeX - Entry
@InProceedings{frer_et_al:LIPIcs:2020:12459,
author = {Martin F{\"u}rer and Carlos Hoppen and Vilmar Trevisan},
title = {{Efficient Diagonalization of Symmetric Matrices Associated with Graphs of Small Treewidth}},
booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
pages = {52:1--52:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-138-2},
ISSN = {1868-8969},
year = {2020},
volume = {168},
editor = {Artur Czumaj and Anuj Dawar and Emanuela Merelli},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12459},
URN = {urn:nbn:de:0030-drops-124590},
doi = {10.4230/LIPIcs.ICALP.2020.52},
annote = {Keywords: Treewidth, Diagonalization, Eigenvalues}
}
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Keywords: |
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Treewidth, Diagonalization, Eigenvalues |
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Collection: |
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47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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29.06.2020 |
