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Dynamic matrix rank with partial lookahead

Author Telikepalli Kavitha



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Telikepalli Kavitha

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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

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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