Abstract
For k (possibly overlap**) polygons of total complexity n in the plane, we present an algorithm for computing a minimum-width square annulus that intersects all input polygons in \(O(n^2\alpha (n)\log ^3 n)\) time, where \(\alpha (\cdot )\) is the inverse Ackermann function. When input polygons are pairwise disjoint, the running time becomes \(O(n\log ^3 n)\). We also present an algorithm for computing a minimum-width square annulus for k convex polygons of total complexity n. The running times are \(O(n\log k)\) for possibly overlap** convex polygons and \(O(n+k\log n)\) for pairwise disjoint convex polygons.
This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the SW Starlab support program (IITP–2017–0–00905) supervised by the IITP (Institute for Information & communications Technology Promotion.).
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Ahn, HK., Ahn, T., Choi, J., Kim, M., Oh, E. (2018). Minimum-Width Square Annulus Intersecting Polygons. In: Rahman, M., Sung, WK., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2018. Lecture Notes in Computer Science(), vol 10755. Springer, Cham. https://doi.org/10.1007/978-3-319-75172-6_6
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