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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)

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)

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)

We propose to design new algorithms for motion planning problems using the well-known Domain Subdivision paradigm, coupled with "soft" predicates. Unlike the traditional exact predicates in computational geometry, our primitives are only exact in the limit. We introduce the notion of resolution-exact algorithms in motion planning: such an algorithm has an… (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)

In this paper we give I/O-optimal techniques for the extraction of isosurfaces from volumetric data, by a novel application of the UO-optimal interval tree of Arge aud Vitter. The main idea is to prepm-cess the dataset once anal for all to build au efficient search strut-ture in disk, aud then each time we want to extract au isosurface, we perform au… (More)

We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map M with n vertices, and apply it to the development of a uniied dynamic data structure that supports point-location, ray-shooting, and shortest-path queries in M. The space requirement is O(n logn). Point-location queries take time O(log n).… (More)

In this paper, we propose a novel technique for constructing multiple levels of a tetrahedral volume dataset while preserving the topologies of all isosurfaces embedded in the data. Our simplification technique has two major phases. In the segmentation phase, we segment the volume data into topological-equivalence regions, that is, the sub-volumes within… (More)