License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2008.1759
URN: urn:nbn:de:0030-drops-17594
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1759/
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Kavitha, Telikepalli

Dynamic matrix rank with partial lookahead

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08004.KavithaTelikepalli.1759.pdf (0.4 MB)

Abstract

We consider the problem of maintaining information about the
rank of a matrix $M$ under changes to its entries. For an $n \times n$ matrix $M$,
we show an amortized upper
bound of $O(n^{\omega-1})$ arithmetic operations per change for
this problem, where $\omega < 2.376$ is the exponent for matrix
multiplication, under the assumption that there is a {\em lookahead}
of up to $\Theta(n)$ locations. That is, we know up to the next $\Theta(n)$
locations $(i_1,j_1),(i_2,j_2),\ldots,$ whose entries
are going to change, in advance; however we do not know the new entries
in these locations in advance. We get the new entries in these
locations in a dynamic manner.

BibTeX - Entry

@InProceedings{kavitha:LIPIcs:2008:1759,
  author =	{Telikepalli Kavitha},
  title =	{{Dynamic matrix rank with partial lookahead}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{268--279},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Ramesh Hariharan and Madhavan Mukund and V Vinay},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1759},
  URN =		{urn:nbn:de:0030-drops-17594},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1759},
  annote =	{Keywords: Matrix rank, dynamic algorithm, fast matrix multiplication}
}

Keywords: Matrix rank, dynamic algorithm, fast matrix multiplication
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Issue Date: 2008
Date of publication: 05.12.2008

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