GD 2012: Graph Drawing pp 303-314

# Covering Paths for Planar Point Sets

• Csaba D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)

## Abstract

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/logn) 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 logn) time in the worst case.

## Keywords

Straight Line Segment Steiner Point Simple Polygon Supporting Line Left Endpoint
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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