Given a set of points, a covering path is a directed polygonal path that visits all the points. We show that for any n points in the plane, there exists a (possibly self-crossing) covering path consisting of n/2 + O(n/log n) straight line segments. If no three points are collinear, any covering path (self-crossing or non-crossing) needs at least n/2 segments. If the path is required to be non-crossing, n - 1 straight line segments obviously suffice and we exhibit n-element point sets which require at least 5n/9 - O(1) segments in any such path. Further, we show that computing a non-crossing covering path for n points in the plane requires Ω(n log n) time in the worst case. © 2013 Springer-Verlag.
CITATION STYLE
Dumitrescu, A., & Tóth, C. D. (2013). Covering paths for planar point sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7704 LNCS, pp. 303–314). https://doi.org/10.1007/978-3-642-36763-2_27
Mendeley helps you to discover research relevant for your work.