Cache-Oblivious Parallel Convex Hull in the Binary Forking Model

Abstract: 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, $O(\log n \log \log n)$ span, and $O(n/B \log_M n)$ serial cache complexity. Here $M$ is the size of the private cache.