Results 1  10
of
3,557
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
Abstract

Cited by 534 (11 self)
 Add to MetaCart
The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms
Optimal search in planar subdivisions
 SIAM JOURNAL OF COMPUTING, VOLTUNE
, 1983
"... A planar subdivision is any partition of the plane into (possibly unbounded) polygonal regions. The subdivision search problem is the following: given a subdivision S with n line segments and a query point P, determine which region of S contains P. We present a practical algorithm for subdivision s ..."
Abstract

Cited by 273 (3 self)
 Add to MetaCart
A planar subdivision is any partition of the plane into (possibly unbounded) polygonal regions. The subdivision search problem is the following: given a subdivision S with n line segments and a query point P, determine which region of S contains P. We present a practical algorithm for subdivision
Planar Point Location Using Persistent Search Trees
, 1986
"... A classical problem in computational geometry is the planar point location problem. This problem calls for preprocessing a polygonal subdivision of the plane defined by n line segments so that, given a sequence of points, the polygon containing each point can be determined quickly online. Several ..."
Abstract

Cited by 177 (4 self)
 Add to MetaCart
A classical problem in computational geometry is the planar point location problem. This problem calls for preprocessing a polygonal subdivision of the plane defined by n line segments so that, given a sequence of points, the polygon containing each point can be determined quickly on
FULLY DYNAMIC POINT LOCATION IN A MONOTONE SUBDIVISION
, 1989
"... In this paper a dynamic technique for locating a point in a monotone planar subdivision, whose current number of vertices is n, is presented. The (complete set of) update operations are insertion of a point on an edge and of a chain of edges between two vertices, and their reverse operations. The d ..."
Abstract

Cited by 23 (7 self)
 Add to MetaCart
In this paper a dynamic technique for locating a point in a monotone planar subdivision, whose current number of vertices is n, is presented. The (complete set of) update operations are insertion of a point on an edge and of a chain of edges between two vertices, and their reverse operations
Point location in disconnected planar subdivisions
, 2010
"... Let G be a (possibly disconnected) planar subdivision and let D be a probability measure over R2. The current paper shows how to preprocess (G,D) into an O(n) size data structure that can answer planar point location queries over G. The expected query time of this data structure, for a query point ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Let G be a (possibly disconnected) planar subdivision and let D be a probability measure over R2. The current paper shows how to preprocess (G,D) into an O(n) size data structure that can answer planar point location queries over G. The expected query time of this data structure, for a query
I/OEfficient Dynamic Planar Point Location
"... We present the first provably I/Oefficient dynamic data structure for point location in a general planar subdivision. Our structure uses O(N/B) disk blocks to store a subdivision of size N , where B is the disk block size. Queries can be answered in ... I/Os in the worstcase, and insertions and de ..."
Abstract

Cited by 31 (15 self)
 Add to MetaCart
We present the first provably I/Oefficient dynamic data structure for point location in a general planar subdivision. Our structure uses O(N/B) disk blocks to store a subdivision of size N , where B is the disk block size. Queries can be answered in ... I/Os in the worstcase, and insertions
Dynamization of the Trapezoid Method for Planar Point Location
, 1991
"... We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point
Improved Dynamic Planar Point Location (Extended Abstract)
"... We develop the first linearspace data structures for dynamic planar point location in general subdivisions that achieve logarithmic query time and polylogarithmic update time. ..."
Abstract
 Add to MetaCart
We develop the first linearspace data structures for dynamic planar point location in general subdivisions that achieve logarithmic query time and polylogarithmic update time.
Dynamic Trees and Dynamic Point Location
 In Proc. 23rd Annu. ACM Sympos. Theory Comput
, 1991
"... This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using ..."
Abstract

Cited by 45 (9 self)
 Add to MetaCart
This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered
ENTROPY, TRIANGULATION, AND POINT LOCATION IN PLANAR SUBDIVISIONS
, 2009
"... A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More specifically, an algorithm is presented that preprocesses a connecte ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More specifically, an algorithm is presented that preprocesses a
Results 1  10
of
3,557