b'@online{MSWClustering2013,'b'\nTITLE = {From Approximate Factorization to Root Isolation with Application to Cylindrical Algebraic Decomposition},\nAUTHOR = {Mehlhorn, Kurt and Sagraloff, Michael and Wang, Pengming},\nLANGUAGE = {eng},\nURL = {http://arxiv.org/abs/1301.4870},\nEPRINT = {1301.4870},\nEPRINTTYPE = {arXiv},\nYEAR = {2013},\nABSTRACT = {We present an algorithm for isolating the roots of an arbitrary complex polynomial $p$ that also works for polynomials with multiple roots provided that the number $k$ of distinct roots is given as part of the input. It outputs $k$ pairwise disjoint disks each containing one of the distinct roots of $p$, and its multiplicity. The algorithm uses approximate factorization as a subroutine. In addition, we apply the new root isolation algorithm to a recent algorithm for computing the topology of a real planar algebraic curve specified as the zero set of a bivariate integer polynomial and for isolating the real solutions of a bivariate polynomial system. For input polynomials of degree $n$ and bitsize $\\tau$, we improve the currently best running time from $\\tO(n^{9}\\tau+n^{8}\\tau^{2})$ (deterministic) to $\\tO(n^{6}+n^{5}\\tau)$ (randomized) for topology computation and from $\\tO(n^{8}+n^{7}\\tau)$ (deterministic) to $\\tO(n^{6}+n^{5}\\tau)$ (randomized) for solving bivariate systems.},\n}\n'