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We present a number of efficient parallel algorithms for constructing 2- and 3-dimensional convex hulls on a randomized CRCW PRAM. Specifically, we show how to build the convex hull of n pre-sorted points in the plane almost surely in O(1) time using O(n log n) processors, or, alternately, almost surely in O(log” n) time using an optimal number of processors. We also show how to find the convex hull of n unsorted points in R2 (resp., 3?s) in O(log n) time using O(n log h) work (resp., 0(log2 n) time using O(min{n logz h, n log n}) work), with very high probability, where h is the number of edges in the convex hull (h is O(n), but can be as small as O(l)). Our algorithms for unsorted input depend on the use of new in-place procedures, that is, procedures that are defined on a subset of elements in the input and that work without re-ordering the input. For the pre-sorted case we also exploit a technique that allows one to modify an algorithm that assumes it is given points so that it can be used on hulls; we call such algorithms point-loll invariant.

In-place techniques for parallel convex hull algorithms (preliminary version)