%0 Journal Article
%T Curves That Must Be Retraced
%A Xiaoyang Gu
%A Jack H. Lutz
%A Elvira Mayordomo
%J Computer Science
%D 2008
%I arXiv
%X We exhibit a polynomial time computable plane curve GAMMA that has finite length, does not intersect itself, and is smooth except at one endpoint, but has the following property. For every computable parametrization f of GAMMA and every positive integer n, there is some positive-length subcurve of GAMMA that f retraces at least n times. In contrast, every computable curve of finite length that does not intersect itself has a constant-speed (hence non-retracing) parametrization that is computable relative to the halting problem.
%U http://arxiv.org/abs/0802.4312v2