In the past 20 years there has been treftlendous progress in developing and analyzing parallel algorithftls. Researchers have developed efficient parallel algorithms to solve most problems for which efficient sequential solutions are known. Although some ofthese algorithms are efficient only in a theoretical framework, many are quite efficient in practice or have key ideas that have been used in efficient implementations. This research on parallel algorithms has not only improved our general understanding ofparallelism but in several cases has led to improvements in sequential algorithms. Unf:ortunately there has been less success in developing good languages f:or prograftlftling parallel algorithftls, particularly languages that are well suited for teaching and prototyping algorithms. There has been a large gap between languages

Abstract. Let P be a set of n points in ~d (where d is a small fixed positive integer), and let F be a collection of subsets of ~d, each of which is defined by a constant number of bounded degree polynomial inequalities. We consider the following F-range searching problem: Given P, build a data structure for efficient answering of queries of the form, &quot;Given a 7 ~ F, count (or report) the points of P lying in 7.&quot; Generalizing the simplex range searching techniques, we give a solution with nearly linear space and preprocessing time and with O(n 1- x/b+~) query time, where d < b < 2d- 3 and ~> 0 is an arbitrarily small constant. The acutal value of b is related to the problem of partitioning arrangements of algebraic surfaces into cells with a constant description complexity. We present some of the applications of F-range searching problem, including improved ray shooting among triangles in ~3 1.

This report describes Nesl, a strongly-typed, applicative, data-parallel language. Nesl is intended to be used as a portable interface for programming a variety of parallel and vector supercomputers, and as a basis for teaching parallel algorithms. Parallelism is supplied through a simple set of data-parallel constructs based on vectors, including a mechanism for applying any function over the elements of a vector in parallel, and a broad set of parallel functions that manipulate vectors. Nesl fully supports nested vectors and nested parallelism---the ability to take a parallel function and then apply it over multiple instances in parallel. Nested parallelism is important for implementing algorithms with complex and dynamically changing data structures, such as required in many graph or sparse matrix algorithms. Nesl also provides a mechanism for calculating the asymptotic running time for a program on various parallel machine models, including the parallel random access machine (PRAM...

The skyline of a d-dimensional dataset contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive methods that can quickly return the initial results without reading the entire database. All the existing algorithms, however, have some serious shortcomings which limit their applicability in practice. In this article we develop branch-andbound skyline (BBS), an algorithm based on nearest-neighbor search, which is I/O optimal, that is, it performs a single access only to those nodes that may contain skyline points. BBS is simple to implement and supports all types of progressive processing (e.g., user preferences, arbitrary dimensionality, etc). Furthermore, we propose several interesting variations of skyline computation, and show how BBS can be applied for their efficient processing.

We present a novel approach to producing facial expression animations for new models. Instead of creating new facial animations from scratch for each new model created, we take advantage of existing animation data in the form of vertex motion vectors. Our method allows animations created by any tools or methods to be easily retargeted to new models. We call this process expression cloning and it provides a new alternative for creating facial animations for character models. Expression cloning makes it meaningful to compile a high-quality facial animation library since this data can be reused for new models. Our method transfers vertex motion vectors from a source face model to a target model having different geometric proportions and mesh structure (vertex number and connectivity). With the aid of an automated heuristic correspondence search, expression cloning typically requires a user to select fewer than ten points in the model. Cloned expression animations preserve the relative motions, dynamics, and character of the original facial animations. CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism Animation; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling Geometric Algorithms; I.2.9 [Artificial Intelligence]: Robotics Kinematics and dynamics Keywords: Deformations, Facial animation, Morphing, Neural Nets 1

In this paper, we show that the universal covering space of a surface can be used to unify previous results on computing paths in a simple polygon. We optimize a given path among obstacles in the plane under the Euclidean and link metrics and under polygonal convex distance functions. Besides revealing connections between the minimum paths under these three distance functions, the framework provided by the universal cover leads to simplified linear-time algorithms for shortest path trees, for minimum-link paths in simple polygons, and for paths restricted to c given orientations. 1 Introduction If a wire, a pipe, or a robot must traverse a path among obstacles in the plane, then one might ask what is the best route to take. For the wire, perhaps the shortest distance is best; for the pipe, perhaps the fewest straight-line segments. For the robot, either might be best depending on the relative costs of turning and moving. In this paper, we find shortest paths and shortest closed curve...

We devise techniques to manipulate a collection of loosely interpenetrating spheres in threedimensional space. Our study is motivated by the representation and manipulation of molecular con gurations, modeled by a collection of spheres. We analyze the sphere model and point toitsfavorable properties that make it more easy to manipulate than an arbitrary collection of spheres. For this special sphere model we present e cient algorithms for computing its union boundary and for hidden surface removal. The e ciency and practicality of our approach are demonstrated by experiments on actual molecule data.

This paper describes the design and implementation of a practical parallel algorithm for Delaunay triangulation that works well on general distributions. Although there have been many theoretical parallel algorithms for the problem, and some implementations based on bucketing that work well for uniform distributions, there has been little work on implementations for general distributions. We use the well known reduction of 2D Delaunay triangulation to find the 3D convex hull of points on a paraboloid. Based on this reduction we developed a variant of the Edelsbrunner and Shi 3D convex hull algorithm, specialized for the case when the point set lies on a paraboloid. This simplification reduces the work required by the algorithm (number of operations) from O(n log^2 n) to O(n log n). The depth (parallel time) is O(log^3 n) on a CREW PRAM. The algorithm is simpler than previous O(n log n) work parallel algorithms leading to smaller constants. Initial experiments using a variety of distributions showed that our parallel algorithm was within a factor of 2 in work from the best sequential algorithm. Based on these promising results, the algorithm was implemented using C and an MPI-based toolkit. Compared with previous work, the resulting implementation achieves significantly better speedups over good sequential code, does not assume a uniform distribution of points, and is widely portable due to its use of MPI as a communication mechanism. Results are presented for the IBM SP2, Cray T3D, SGI Power Challenge, and DEC AlphaCluster.

In the plane, the post-ofice problem, which asks for the closest site to a query site, and retraction motion planning, which asks for a one-dimensional retract of the free space of a robot, are both classt-cally solved by computing a Voronoi diagram. When the sites are k disjoint convex sets, we give a com-pact representation of the Voronoi diagram, using O(k) line segments, that is suficient for logarithmic time post-ofice location queries and motion plan-ning. If these sets are polygons with n total vertices, we compute this diagram optimally in O ( k log n) de-terministic time for the Euclidean metric and in O(k logn logm) deterministic time for the convex distance function defined by a convex m-gon. 1

In this paper, we give an algorithm for output-sensitive construction of an f-face convex hull of a set of n points in general position in E 4 . Our algorithm runs in O((n + f)log 2 f) time and uses O(n + f) space. This is the first algorithm within a polylogarithmic factor of optimal O(n log f + f) time over the whole range of f . By a standard lifting map, we obtain outputsensitive algorithms for the Voronoi diagram or Delaunay triangulation in E 3 and for the portion of a Voronoi diagram that is clipped to a convex polytope. Our approach simplifies the "ultimate convex hull algorithm" of Kirkpatrick and Seidel in E 2 and also leads to improved output-sensitive results on constructing convex hulls in E d for any even constant d ? 4. 1 Introduction Geometric structures induced by n points in Euclidean d-dimensional space, such as the convex hull, Voronoi diagram, or Delaunay triangulation, can be of larger size than the point set that defines them. In many practical situat...