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://drops.dagstuhl.de/opus/volltexte/2008/1759/
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### Dynamic matrix rank with partial lookahead

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### 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},