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Dynamic matrix rank with partial lookahead

Author Telikepalli Kavitha

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LIPIcs.FSTTCS.2008.1759.pdf
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Keywords
  • Matrix rank
  • dynamic algorithm
  • fast matrix multiplication

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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.

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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

Author Details

Telikepalli Kavitha
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