Guest editor's introduction

David Dobkin
1987 Discrete & Computational Geometry  
The first five articles appearing in this special issue are revised and expanded versions of papers that were presented at the ACM SIGGRAPH/SIGACT Symposium on Computational Geometry held June 2-4, 1986, at IBM, Yorktown Heights, New York. They were selected for invitation to the special issue from the 33 papers that were presented at the symposium. These papers had been selected from 100 extended abstracts which were submitted to the conference. The invited articles were chosen for their
more » ... ionally high quality. Emphasis was also placed on choosing papers from the conference which were of great relevance to the goals of this journal and had a component which clearly related to discrete geometry as well as the computational geometry component. The final paper on this issue is included here because of its similarity to those which constitute the special issue. The first paper, "Triangulating Point Sets in Space" by Avis and EIGindy, considers the problem of triangulating a set of simplicial (i.e., exactly d + 1 of a set of n points in Euclidean d-space lie on the convex hull) points. They introduce the notion of a "splitter" being a point which partitions a simplex into subsimplices such that a positive fraction of the points avoid each subsimplex. This property provides the possibility that their technique will find application in higherdimensional divide-and-conquer algorithms which depend upon such a subdivision. The next two papers, "Linear Space Data Structures for Two Types of Range Search" by Chazelle and Edelsbrunner and "e-Nets and Simplex Range Queries" by Haussler and Welzt, deal with problems related to range searching. Chazelle and Edelsbrunner consider the problem of building linear space search structures for two specific range-searching problems. They consider the problems of homothetic range searching in the plane and domination range searching in three dimensions. Their first result is optimal in time and space, their second is optimal in space and within a factor of log n of being optimal in time. Both of their results relate to the problem of finding good partitions of point sets in Euclidian n-space. Haussler and Welzl consider this problem and provide significant improvements over previous results. By relating this problem to the Vapnik-Chervonenkis dimension of a range domain, they are able to produce a structure
doi:10.1007/bf02187873 fatcat:zud2ny7jkffhle7pahrtkjrlgu