Orthogonal Range Searching

1997 ◽  
pp. 93-117
Author(s):  
Mark de Berg ◽  
Marc van Kreveld ◽  
Mark Overmars ◽  
Otfried Schwarzkopf
Keyword(s):  
Range Searching ◽  
Orthogonal Range Searching

scholarly journals Multivariate Analysis of Orthogonal Range Searching and Graph Distances

Algorithmica ◽  
2020 ◽  
Vol 82 (8) ◽  
pp. 2292-2315
Author(s):  
Karl Bringmann ◽  
Thore Husfeldt ◽  
Måns Magnusson
Keyword(s):  
Multivariate Analysis ◽  
Range Searching ◽  
Orthogonal Range Searching ◽  
Graph Distances

Orthogonal Range Searching

2000 ◽  
pp. 95-120 ◽  
Author(s):  
Mark de Berg ◽  
Marc van Kreveld ◽  
Mark Overmars ◽  
Otfried Cheong Schwarzkopf
Keyword(s):  
Range Searching ◽  
Orthogonal Range Searching

GENERALIZED INTERSECTION SEARCHING PROBLEMS

1993 ◽  
Vol 03 (01) ◽  
pp. 39-69 ◽  
Author(s):  
RAVI JANARDAN ◽  
MARIO LOPEZ
Keyword(s):  
Query Time ◽  
Range Searching ◽  
New Class ◽  
Standard Problem ◽  
Geometric Objects ◽  
Intersection Searching ◽  
Orthogonal Range Searching ◽  
Point Enclosure

A new class of geometric intersection searching problems is introduced, which generalizes previously-considered intersection searching problems and is rich in applications. In a standard intersection searching problem, a set S of n geometric objects is to be preprocessed so that the objects that are intersected by a query object q can be reported efficiently. In a generalized problem, the objects in S come aggregated in disjoint groups and what is of interest are the groups, not the objects, that are intersected by q. Although this problem can be solved easily by using an algorithm for the standard problem, the query time can be Ω(n) even though the output size is just O(1). In this paper, algorithms with efficient, output-size-sensitive query times are presented for the generalized versions of a number of intersection searching problems, including: interval intersection searching, orthogonal segment intersection searching, orthogonal range searching, point enclosure searching, rectangle intersection searching, and segment intersection searching. In addition, the algorithms are also space-efficient.

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