{"title":"A worst case bound for topology computation of algebraic curves","quality_controlled":"1","status":"public","year":"2012","publisher":"Elsevier","scopus_import":1,"intvolume":"        47","oa_version":"Preprint","oa":1,"date_created":"2018-12-11T12:02:43Z","volume":47,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publist_id":"3303","_id":"3331","department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"main_file_link":[{"url":"http://arxiv.org/abs/1104.1510","open_access":"1"}],"abstract":[{"lang":"eng","text":"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."}],"citation":{"short":"M. Kerber, M. Sagraloff,  Journal of Symbolic Computation 47 (2012) 239–258.","apa":"Kerber, M., &#38; Sagraloff, M. (2012). A worst case bound for topology computation of algebraic curves. <i> Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jsc.2011.11.001\">https://doi.org/10.1016/j.jsc.2011.11.001</a>","ista":"Kerber M, Sagraloff M. 2012. A worst case bound for topology computation of algebraic curves.  Journal of Symbolic Computation. 47(3), 239–258.","chicago":"Kerber, Michael, and Michael Sagraloff. “A Worst Case Bound for Topology Computation of Algebraic Curves.” <i> Journal of Symbolic Computation</i>. Elsevier, 2012. <a href=\"https://doi.org/10.1016/j.jsc.2011.11.001\">https://doi.org/10.1016/j.jsc.2011.11.001</a>.","ama":"Kerber M, Sagraloff M. A worst case bound for topology computation of algebraic curves. <i> Journal of Symbolic Computation</i>. 2012;47(3):239-258. doi:<a href=\"https://doi.org/10.1016/j.jsc.2011.11.001\">10.1016/j.jsc.2011.11.001</a>","ieee":"M. Kerber and M. Sagraloff, “A worst case bound for topology computation of algebraic curves,” <i> Journal of Symbolic Computation</i>, vol. 47, no. 3. Elsevier, pp. 239–258, 2012.","mla":"Kerber, Michael, and Michael Sagraloff. “A Worst Case Bound for Topology Computation of Algebraic Curves.” <i> Journal of Symbolic Computation</i>, vol. 47, no. 3, Elsevier, 2012, pp. 239–58, doi:<a href=\"https://doi.org/10.1016/j.jsc.2011.11.001\">10.1016/j.jsc.2011.11.001</a>."},"date_published":"2012-03-01T00:00:00Z","publication_status":"published","issue":"3","month":"03","date_updated":"2021-01-12T07:42:43Z","type":"journal_article","publication":" Journal of Symbolic Computation","author":[{"full_name":"Kerber, Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299"},{"first_name":"Michael","last_name":"Sagraloff","full_name":"Sagraloff, Michael"}],"day":"01","page":"239 - 258","doi":"10.1016/j.jsc.2011.11.001"}