Efficient diagonalization of symmetric matrices associated with graphs of small treewidth

Martin Fürer, Carlos Hoppen, Vilmar Trevisan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Let M = (mij) 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 mij 6= 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 T of width k, then this can be done in time O(k|T | + k2n), where |T | denotes the number of nodes in T .

Original languageEnglish (US)
Title of host publication47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
EditorsArtur Czumaj, Anuj Dawar, Emanuela Merelli
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771382
DOIs
StatePublished - Jun 1 2020
Event47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 - Virtual, Online, Germany
Duration: Jul 8 2020Jul 11 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume168
ISSN (Print)1868-8969

Conference

Conference47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
CountryGermany
CityVirtual, Online
Period7/8/207/11/20

All Science Journal Classification (ASJC) codes

  • Software

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