Under the promise that the convex hull vertices form a subsequence of the input, the hull can be computed in O(n sqrt(log n)) deterministic time or O(n log^ε n) expected time, and the promise is tight because even one out-of-order hull point forces an Omega(n log n) lower bound.
40Ivor van der Hoog, Henrik Reinstädtler, and Eva Rotenberg
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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cs.CG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Quadtrees and related structures are 2-Presortable, admitting expected O(n sqrt(log n)) algorithms given presorts along both axes.
citing papers explorer
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Computing Planar Convex Hulls with a Promise
Under the promise that the convex hull vertices form a subsequence of the input, the hull can be computed in O(n sqrt(log n)) deterministic time or O(n log^ε n) expected time, and the promise is tight because even one out-of-order hull point forces an Omega(n log n) lower bound.
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The Presort Hierarchy for Geometric Problems
Quadtrees and related structures are 2-Presortable, admitting expected O(n sqrt(log n)) algorithms given presorts along both axes.