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STACS
1999
Springer

Lower Bounds for Dynamic Algebraic Problems

9 years 3 months ago
Lower Bounds for Dynamic Algebraic Problems
Abstract. We consider dynamic evaluation of algebraic functions (matrix multiplication, determinant, convolution, Fourier transform, etc.) in the model of Reif and Tate; i.e., if f(x1, . . . , xn) = (y1, . . . , ym) is an algebraic problem, we consider serving on-line requests of the form “change input xi to value v” or “what is the value of output yi?”. We present techniques for showing lower bounds on the worst case time complexity per operation for such problems. The first gives lower bounds in a wide range of rather powerful models (for instance history dependent algebraic computation trees over any infinite subset of a field, the integer RAM, and the generalized real RAM model of Ben-Amram and Galil). Using this technique, we show optimal Ω(n) bounds for dynamic matrix-vector product, dynamic matrix multiplication and dynamic discriminant and an Ω( √ n) lower bound for dynamic polynomial multiplication (convolution), providing a good match with Reif and Tate’s O...
Gudmund Skovbjerg Frandsen, Johan P. Hansen, Peter
Added 05 Aug 2010
Updated 05 Aug 2010
Type Conference
Year 1999
Where STACS
Authors Gudmund Skovbjerg Frandsen, Johan P. Hansen, Peter Bro Miltersen
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