LIPIcs.FSTTCS.2008.1759.pdf
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Dynamic matrix rank with partial lookahead
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IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2008-12-05
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Telikepalli Kavitha. Dynamic matrix rank with partial lookahead. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 268-279, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1759
https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1759
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.
Keywords
- Matrix rank
- dynamic algorithm
- fast matrix multiplication
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