Learn More
We present linear-space sub-logarithmic algorithms for handling the 3-dimensional dominance reporting and the 2-dimensional dominance counting problems. Under the RAM model as described in [M. L. Fredman and D. E. Willard. “Surpassing the information theoretic bound with fusion trees”, Journal of Computer and System Sciences, 47:424– 436, 1993], our(More)
We propose a novel persistent octree (POT) indexing structure for accelerating isosurface extraction and spatial filtering from volumetric data. This data structure efficiently handles a wide range of visualization problems such as the generation of view-dependent isosurfaces, ray tracing, and isocontour slicing for high dimensional data. POT can be viewed(More)
We present in this paper fast algorithms for the 3-D dominance reporting and counting problems, and generalize the results to the d-dimensional case. Our 3-D dominance reporting algorithm achieves O(log n= log log n + f) 1 query time using O(n log n) space , where f is the number of points satisfying the query and > 0 is an arbitrarily small constant. For(More)
Using the notions of Q heaps and fusion trees developed by Fredman and Willard we develop a faster version of the fractional cascading technique while maintaining the linear space structure The new version enables sublogarithmic iterative search in the case when we have a search tree and the degree of each node is bounded by O log n for some constant where(More)
Given a set of n objects each characterized by d attributes speci ed at m xed time instances we are interested in the problem of designing space e cient indexing structures such that arbitrary temporal range search queries can be handled e ciently When m our problem reduces to the d dimensional orthogonal search problem We establish e cient data structures(More)
We introduce the Persistent HyperOcTree (PHOT) to handle the 4D isocontouring problem for large scale time-varying data sets. This novel data structure is provably space efficient and optimal in retrieving active cells. More importantly, the set of active cells for any possible isovalue are already organized in a Compact Hyperoctree, which enables very(More)
Using the notions of Q-heaps and fusion trees developed by Fredman and Willard, we develop general transformation techniques to reduce a number of computational geometry problems to their special versions in partially ranked spaces. In particular, we develop a fast fractional cascading technique, which uses linear space and enables sublogarithmic iterative(More)