Cache-Oblivious Output-Sensitive Two-Dimensional Convex Hull

We consider the problem of two-dimensional outputsensitive convex hull in the cache-oblivious model. That is, we are interested in minimizing the number of cache faults caused when computing the convex hull of a set of N points on a plane. We are interested in the outputsensitive case where number of cache misses are analyzed in the worst case based on both the input size N and output size H (number of extreme points that lie on the final convex hull ). There is the lower bound of N B logM B H B to match where M is the cache size and B is the block size. We present a simple algorithm which almost matches this lower bound. The number of cache misses our algorithm causes is O max N B log log M B , N B logM B H B . Thus, it can only be an additional term N B log log M B away from the optimal.

• Type: Conference
• Year: 2007
• Where: CCCG
• Authors: Peyman Afshani, Arash Farzan
• Keywords: Cache, Cache Misses, CCCG 2007, Computational Geometry, Convex Hull