A worst case bound for topology computation of algebraic curves

M. Kerber, M. Sagraloff, Journal of Symbolic Computation 47 (2012) 239–258.


Journal Article | Published | English
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Department
Abstract
Computing the topology of an algebraic plane curve C means computing a combinatorial graph that is isotopic to C and thus represents its topology in R2. We prove that, for a polynomial of degree n with integer coefficients bounded by 2ρ, the topology of the induced curve can be computed with bit operations ( indicates that we omit logarithmic factors). Our analysis improves the previous best known complexity bounds by a factor of n2. The improvement is based on new techniques to compute and refine isolating intervals for the real roots of polynomials, and on the consequent amortized analysis of the critical fibers of the algebraic curve.
Publishing Year
Date Published
2012-03-01
Journal Title
Journal of Symbolic Computation
Volume
47
Issue
3
Page
239 - 258
IST-REx-ID

Cite this

Kerber M, Sagraloff M. A worst case bound for topology computation of algebraic curves. Journal of Symbolic Computation. 2012;47(3):239-258. doi:10.1016/j.jsc.2011.11.001
Kerber, M., & Sagraloff, M. (2012). A worst case bound for topology computation of algebraic curves. Journal of Symbolic Computation, 47(3), 239–258. https://doi.org/10.1016/j.jsc.2011.11.001
Kerber, Michael, and Michael Sagraloff. “A Worst Case Bound for Topology Computation of Algebraic Curves.” Journal of Symbolic Computation 47, no. 3 (2012): 239–58. https://doi.org/10.1016/j.jsc.2011.11.001.
M. Kerber and M. Sagraloff, “A worst case bound for topology computation of algebraic curves,” Journal of Symbolic Computation, vol. 47, no. 3, pp. 239–258, 2012.
Kerber M, Sagraloff M. 2012. A worst case bound for topology computation of algebraic curves. Journal of Symbolic Computation. 47(3), 239–258.
Kerber, Michael, and Michael Sagraloff. “A Worst Case Bound for Topology Computation of Algebraic Curves.” Journal of Symbolic Computation, vol. 47, no. 3, Elsevier, 2012, pp. 239–58, doi:10.1016/j.jsc.2011.11.001.

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