Cache-Oblivious Parallel Convex Hull in the Binary Forking Model

05/17/2023

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by   Reilly Browne, et al.

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We present two cache-oblivious sorting-based convex hull algorithms in the Binary Forking Model. The first is an algorithm for a presorted set of points which achieves O(n) work, O(log n) span, and O(n/B) serial cache complexity, where B is the cache line size. These are all optimal worst-case bounds for cache-oblivious algorithms in the Binary Forking Model. The second adapts Cole and Ramachandran's cache-oblivious sorting algorithm, matching its properties including achieving O(n log n) work, O(log n loglog n) span, and O(n/B log_M n) serial cache complexity. Here M is the size of the private cache.