results for au:Amenta_N in:cs
Jul 19 2017 cs.DC
We develop and implement a concurrent dictionary data structure based on the Log Structured Merge tree (LSM), suitable for current massively parallel GPU architectures. Our GPU LSM is dynamic (mutable) in that it provides fast updates (insertions and deletions). For example, on an NVIDIA K40c GPU we can get an average update rate of 225 M elements/s (13.5x faster than merging with a sorted array). GPU LSM also supports lookup, count, and range query operations with an average rate of 75 M, 32 M and 23 M queries/s respectively. For lookups, we are 7.5x (and 1.75x) slower than a hash table (and a sorted array). However, none of these other data structures are considered mutable, and hash tables cannot even support count and range queries. We believe that our GPU LSM is the first dynamic general-purpose GPU data structure.
Aug 05 2014 cs.CG
The change in the normal between any two nearby points on a closed, smooth surface is bounded with respect to the local feature size (distance to the medial axis). An incorrect proof of this lemma appeared as part of the analysis of the "crust" algorithm of Amenta and Bern.
Here we present the results of the NSF-funded Workshop on Computational Topology, which met on June 11 and 12 in Miami Beach, Florida. This report identifies important problems involving both computation and topology.
Sep 26 1998 cs.CG
We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using generalized linear programming. We also give efficient algorithms for some mesh smoothing problems that do not fit into the generalized linear programming paradigm.
We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.