Abstract
Given a rectilinear polygon P and a point \(p \in P\), what is a largest axis-parallel square in P that contains p? This question arises in VLSI design from physical limitations of manufacturing processes. Related problems with disks instead of squares and point sets instead of polygons have been studied previously.
We present an efficient algorithm to preprocess P in time O(n) for simple polygons or \(O(n \log n)\) if holes are allowed. The resulting data structure of size O(n) can be used to answer largest square queries for any point in P in time \(O(\log n)\). Given a set of points Q instead of a rectilinear polygon, the same algorithm can be used to find a largest square containing a given query point but not containing any point in Q in its interior.
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Gester, M., Hähnle, N., Schneider, J. (2015). Largest Empty Square Queries in Rectilinear Polygons. In: Gervasi, O., et al. Computational Science and Its Applications -- ICCSA 2015. ICCSA 2015. Lecture Notes in Computer Science(), vol 9155. Springer, Cham. https://doi.org/10.1007/978-3-319-21404-7_20
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DOI: https://doi.org/10.1007/978-3-319-21404-7_20
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