Faster Algorithms for Largest Empty Rectangles and Boxes

نویسندگان

چکیده

We revisit a classical problem in computational geometry: finding the largest-volume axis-aligned empty box (inside given bounding box) amidst n points d dimensions. Previously, best algorithms known have running time $$O(n\log ^2n)$$ for $$d=2$$ (Aggarwal and Suri 1987) near $$n^d$$ $$d\ge 3$$ . describe faster with following times (where $$\varepsilon >0$$ is an arbitrarily small constant $$\widetilde{O}$$ hides polylogarithmic factors): To obtain higher-dimensional result, we adapt extend previous techniques Klee’s measure to optimize certain objective functions over complement of union orthants.

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ژورنال

عنوان ژورنال: Discrete and Computational Geometry

سال: 2023

ISSN: ['1432-0444', '0179-5376']

DOI: https://doi.org/10.1007/s00454-022-00473-x