In this paper, we study the problem of computing a minimum-width double-strip or parallelogram annulus that encloses a given set of n points in the plane. A double-strip is a closed region in the plane whose boundary consists of four parallel lines and a parallelogram annulus is a closed region between two edge-parallel parallelograms. We present several first algorithms for these problems. Among them are O(n^2) and O(n^3 log n)-time algorithms that compute a minimum-width double-strip and parallelogram annulus, respectively, when their orientations can be freely chosen.
@InProceedings{bae:LIPIcs.ISAAC.2019.25, author = {Bae, Sang Won}, title = {{Minimum-Width Double-Strip and Parallelogram Annulus}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {25:1--25:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Lu, Pinyan and Zhang, Guochuan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.25}, URN = {urn:nbn:de:0030-drops-115211}, doi = {10.4230/LIPIcs.ISAAC.2019.25}, annote = {Keywords: geometric covering, parallelogram annulus, two-line center, double-strip} }
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