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We present a collection of new techniques for designing and analyzing eecient external-memory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of speciic problems. Our results include: Proximate-neighboring. We present a simple method for deriving external-memory lower bounds via reductions from a problem we(More)
We consider the two-point query version of the fundamental geometric shortest path problem: Given a set h of polygonal obstacles iu the plane, having a total of n vertices, build a data structure such that for any two query points s and t we can efficiently determine the length, d(s,t), of an Euclidean shortest obstacle-avoiding path, *(s,t), from s to t.(More)
Contour trees are used when high-dimensional data are preprocessed for efficient extraction of isocontours for the purpose of visualization. So far, efficient algorithms for contour trees are based on processing the data in sorted order. We present a new algorithm that avoids sorting of the whole dataset, but sorts only a subset of so-called(More)
In this paper, we present a novel out-of-core technique for the interactive computation of isosurfaces from volume data. Our algorithm minimizes the main memory and disk space requirements on the visualization workstation, while speeding up isosurface extraction queries. Our overall approach is a two-level indexing scheme. First, by our meta-cell technique,(More)
In this paper we give I/O-optimal techniques for the extraction of isosurfaces from volumetric data, by a novel application of the I/O-optimal interval tree of Arge and Vitter. The main idea is to prepro-cess the dataset once and for all to build an efficient search structure in disk, and then each time we want to extract an isosurface, we perform an(More)
Approved for public release; further dissemination unlimited DISCLAIMER This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or(More)
In this paper, we propose a novel external-memory algorithm to support view-dependent simplification for datasets much larger than main memory. In the preprocessing phase, we use a new spanned sub-meshes simplification technique to build view-dependence trees I/O-efficiently, which preserves the correct edge collapsing order and thus assures the run-time(More)
We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map M with 7~ vertices, and apply it to the development of a unified dynamic data structure that supports point-location, ray-shooting, and shortest-path queries in M. The space requirement is O(nlog n). Point-location queries take time O(log 7~).(More)
We consider the problems of conflict detection and resolution in air traffic management (ATM) from the perspective of computational geometry and give algorithms for solving these problems efficiently. For conflict resolution, we propose a simple method that can route multiple aircraft, conflict-free, through a cluttered airspace, using a prioritized routing(More)