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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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.