Dynamic matrix rank with partial lookahead

Kavitha, Telikepalli (2008) Dynamic matrix rank with partial lookahead. In: Foundations of Software Technology and Theoretical Computer Science (Bangalore) 2008, 05.12.2008.

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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.

Item Type:	Conference Paper
Keywords:	Matrix rank;dynamic algorithm;fast matrix multiplication
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	23 Sep 2011 09:20
Last Modified:	23 Sep 2011 09:20
URI:	http://eprints.iisc.ac.in/id/eprint/40704

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