Shortest Path in a Polygon using Sublinear Space
Computational Geometry
2015-12-01 v2
Abstract
\renewcommand{\Re}{{\rm I\!\hspace{-0.025em} R}} \newcommand{\SetX}{\mathsf{X}} \newcommand{\VorX}[1]{\mathcal{V} \pth{#1}} \newcommand{\Polygon}{\mathsf{P}} \newcommand{\Space}{\overline{\mathsf{m}}} \newcommand{\pth}[2][\!]{#1\left({#2}\right)} We resolve an open problem due to Tetsuo Asano, showing how to compute the shortest path in a polygon, given in a read only memory, using sublinear space and subquadratic time. Specifically, given a simple polygon with vertices in a read only memory, and additional working memory of size , the new algorithm computes the shortest path (in ) in expected time. This requires several new tools, which we believe to be of independent interest.
Cite
@article{arxiv.1412.0779,
title = {Shortest Path in a Polygon using Sublinear Space},
author = {Sariel Har-Peled},
journal= {arXiv preprint arXiv:1412.0779},
year = {2015}
}