Computational geometry: an introduction
Computational geometry: an introduction
On-line construction of the convex hull of a simple polyline
Information Processing Letters
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Improved lower bounds for the link length of rectilinear spanning paths in grids
Information Processing Letters
Lectures on Discrete Geometry
Approximation Algorithms for the Minimum Bends Traveling Salesman Problem
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Information Processing Letters
Space-efficient algorithms for computing the convex hull of a simple polygonal line in linear time
Computational Geometry: Theory and Applications
On covering points with minimum turns
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Computational geometry column 54
ACM SIGACT News
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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.