Optimal in-place and cache-oblivious algorithms for 3-d convex hulls and 2-d segment intersection

Optimal Parallel Randomized Algorithms for 3-D Convex Hulls and Related Problems

Cache-Oblivious Red-Blue Line Segment Intersection

We present an optimal cache-oblivious algorithm for finding all intersections between a set of non-intersecting red segments and a set of non-intersecting blue segments in the plane. Our algorithm uses O( B logM/B N B + T/B) memory transfers, where N is the total number of segments, M and B are the memory and block transfer sizes of any two consecutive levels of any multilevel memory hierarchy,...

An Algorithm to Build Convex Hulls for 3-d Objects

In this paper, a new algorithm based on the Quickhull algorithm is proposed to find convex hulls for 3-D objects using neighbor trees. The neighbor tree is the data structure by which all visible facets to the selected furthest outer point can be found. The neighboring sequence of ridges on the outer boundary of all visible facets also can be found directly from the neighbor tree. This new algo...

Cache-oblivious Algorithms Cache-oblivious Algorithms Acknowledgments

This thesis presents “cache-oblivious” algorithms that use asymptotically optimal amounts of work, and move data asymptotically optimally among multiple levels of cache. An algorithm is cache oblivious if no program variables dependent on hardware configuration parameters, such as cache size and cache-line length need to be tuned to minimize the number of cache misses. We show that the ordinary...

Algorithms for 3 D Map Segment Registration

Many applications require dimensionally accurate and detailed maps of the environment. Mobile mapping devices with laser ranging devices can generate highly detailed and dimensionally accurate coordinate data in the form of point clouds. Point clouds represent scenes with numerous discrete coordinate samples obtained about a relative reference frame defined by the location and orientation of th...