Dynamic matrix rank with partial lookahead

We consider the problem of maintaining information about the rank of a matrix M under changes to its entries. For an n × n matrix M, we show an amortized upper bound of O(nω−1) arithmetic operations per change for this problem, where ω < 2.376 is the exponent for matrix multiplication, under the assumption that there is a lookahead of up to Θ(n) locations. That is, we know up to the next Θ(n) locations (i1, j1), (i2, j2), . . . , 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.

• Type: Conference
• Year: 2008
• Where: FSTTCS
• Authors: Telikepalli Kavitha
• Keywords: Amortized Upper Bound, FSTTCS 2008, Matrix, Matrix M, Software Engineering