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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 " , our algorithms achieve O(log n/ log log n + f) query time for the… (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)

- Qingmin Shi, Joseph Jaja
- 2006

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)

- Qingmin Shi, Joseph Jaja
- 2003

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 >… (More)

Given a set of n objects, each characterized by d attributes speciied at m xed time instances, we are interested in the problem of designing space eecient indexing structures such that arbitrary temporal range search queries can be handled eeciently. When m = 1, our problem reduces to the d-dimensional orthogonal search problem. We establish eecient data… (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)

We consider the problem of organizing large scale earth science raster data to ef-ciently handle queries for identifying regions whose parameters fall within certain range values speciied by the queries. This problem seems to be critical to enabling basic data mining tasks such as determining associations between physical phenomena and spatial factors,… (More)