Abstract
We present approximation algorithms for cutting out polygons with line cuts and ray cuts. Our results answer a number of open problems and are either the first solutions or significantly improve over previously known solutions. For the line cutting version, we prove a key property that leads to a simple, constant factor approximation algorithm. For the ray cutting version, we prove it is possible to compute in almost linear time a cutting sequence that is an O(log2 n)-factor approximation. No algorithms were previously known for the ray cutting version.
Keywords
- Convex Polygon
- Dynamic Programming Algorithm
- Factor Approximation
- Constant Factor Approximation
- Plane Sweep
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.
This research was partially supported by NSF grant CCF-0430366.
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© 2004 Springer-Verlag Berlin Heidelberg
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Daescu, O., Luo, J. (2004). Cutting Out Polygons with Lines and Rays. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_58
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DOI: https://doi.org/10.1007/978-3-540-30551-4_58
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24131-7
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