TY - JOUR
AU - Nishimura, Masaki
AU - Ryuichi Shigemoto
AU - Matsubayashi, K
AU - Mimori, Y
AU - Kameyama, Masakuni
ID - 2521
IS - 11
JF - Clinical Neurology
TI - Meningoencephalitis during the pre-icteric phase of hepatitis A - a case report
VL - 27
ER -
TY - BOOK
AB - Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.
AU - Edelsbrunner, Herbert
ID - 3900
SN - 9783540137221
TI - Algorithms in Combinatorial Geometry
VL - 10
ER -
TY - JOUR
AB - The visibility graph of a finite set of line segments in the plane connects two endpoints u and v if and only if the straight line connection between u and v does not cross any line segment of the set. This article proves that 5n - 4 is a lower bound on the number of edges in the visibility graph of n nonintersecting line segments in the plane. This bound is tight.
AU - Herbert Edelsbrunner
AU - Shen, Xiaojun
ID - 4094
IS - 2
JF - Information Processing Letters
TI - A tight lower bound on the size of visibility graphs
VL - 26
ER -
TY - JOUR
AB - he kth-order Voronoi diagram of a finite set of sites in the Euclidean plane E2 subdivides E2 into maximal regions such that all points within a given region have the same k nearest sites. Two versions of an algorithm are developed for constructing the kth-order Voronoi diagram of a set of n sites in O(n2 log n + k(n - k) log2 n) time, O(k(n - k)) storage, and in O(n2 + k(n - k) log2 n) time, O(n2) storage, respectively.
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
ID - 4095
IS - 11
JF - IEEE Transactions on Computers
TI - An improved algorithm for constructing kth-order Voronoi diagrams
VL - 36
ER -
TY - JOUR
AB - This paper investigates the existence of linear space data structures for range searching. We examine thehomothetic range search problem, where a setS ofn points in the plane is to be preprocessed so that for any triangleT with sides parallel to three fixed directions the points ofS that lie inT can be computed efficiently. We also look atdomination searching in three dimensions. In this problem,S is a set ofn points inE 3 and the question is to retrieve all points ofS that are dominated by some query point. We describe linear space data structures for both problems. The query time is optimal in the first case and nearly optimal in the second.
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
ID - 4100
IS - 1
JF - Discrete & Computational Geometry
TI - Linear space data structures for two types of range search
VL - 2
ER -