Showing papers by "Michael T. Goodrich published in 1992"
TL;DR: This work presents algorithms for the well-known hidden-line and hidden-surface elimination problems that are optimal in the worst case, and are also able to take advantage of problem instances that are “simpler” than in the best case.
37 citations
TL;DR: These algorithms provide parallel analogues to well-known phenomena from sequential computational geometry, such as the fact that problems for polygons can oftentimes be solved more efficiently than point-set problems, and that nearest-neighbor problems can be solved without explicitly constructing a Voronoi diagram.
Abstract: In this paper we give parallel algorithms for a number of problems defined on point sets and polygons. All our algorithms have optimalT(n) * P(n) products, whereT(n) is the time complexity andP(n) is the number of processors used, and are for the EREW PRAM or CREW PRAM models. Our algorithms provide parallel analogues to well-known phenomena from sequential computational geometry, such as the fact that problems for polygons can oftentimes be solved more efficiently than point-set problems, and that nearest-neighbor problems can be solved without explicitly constructing a Voronoi diagram.
30 citations
TL;DR: Efficient parallel algorithms for solving a number of visibility and shortest-path problems for simple polygons are given, based on the use of a new data structure for implicitly representing all shortest paths in a simple polygonP, which is thestratified decomposition tree.
Abstract: In this paper we give efficient parallel algorithms for solving a number of visibility and shortest-path problems for simple polygons. Our algorithms all run inO(logn) time and are based on the use of a new data structure for implicitly representing all shortest paths in a simple polygonP, which we call thestratified decomposition tree. We use this approach to derive efficient parallel methods for computing the visibility ofP from an edge, constructing the visibility graph of the vertices ofP (using an output-sensitive number of processors), constructing the shortest-path tree from a vertex ofP, and determining all-farthest neighbors for the vertices inP. The computational model we use is the CREW PRAM.
24 citations
01 Sep 1992
TL;DR: In this paper, the problem of using disk blocks efficiently in searching graphs that are too large to fit in internal memory was considered, where a vertex can be represented any number of times on the disk in order to take advantage of redundancy.
Abstract: In this paper we consider the problem of using disk blocks efficiently in searching graphs that are too large to fit in internal memory. Our model allows a vertex to be represented any number of times on the disk in order to take advantage of redundancy. We give matching upper and lower bounds for complete d-ary trees and d-dimensional grid graphs, as well as for classes of general graphs that intuitively speaking have a close to uniform number of neighbors around each vertex.
1 citations