scholarly journals Higher Order City Voronoi Diagrams

2012 ◽  
pp. 59-70 ◽  
Author(s):  
Andreas Gemsa ◽  
D. T. Lee ◽  
Chih-Hung Liu ◽  
Dorothea Wagner
Keyword(s):  
Voronoi Diagrams ◽  
Higher Order

What-If Emergency Response Through Higher Order Voronoi Diagrams

2009 ◽  
pp. 77-95
Author(s):  
Ickjai Lee ◽  
Reece Pershouse ◽  
Peter Phillips ◽  
Kyungmi Lee ◽  
Christopher Torpelund-Bruin
Keyword(s):  
Emergency Response ◽  
Voronoi Diagrams ◽  
Higher Order

FINDING k FARTHEST PAIRS AND k CLOSEST/FARTHEST BICHROMATIC PAIRS FOR POINTS IN THE PLANE

1995 ◽  
Vol 05 (01n02) ◽  
pp. 37-51 ◽  
Author(s):  
NAOKI KATOH ◽  
KAZUO IWANO
Keyword(s):  
Voronoi Diagrams ◽  
Search Space ◽  
Higher Order ◽  
Efficient Algorithms ◽  
New Technique ◽  
Enumeration Problems ◽  
A New Technique ◽  
Geometric Enumeration

We study the problem of enumerating k farthest pairs for n points in the plane and the problem of enumerating k closest/farthest bichromatic pairs of n red and n blue points in the plane. We propose a new technique for geometric enumeration problems which iteratively reduces the search space by a half and provides efficient algorithms. As applications of this technique, we develop algorithms, using higher order Voronoi diagrams, for the above problems, which run in O(min{n2, n log n+k4/3log n/log1/3 k}) time and O(n+k4/3/log1/3 k+k log n) space for general Lp metric with p≠2, and O(min{n2, n log n+k4/3}) time and O(n+k4/3+k log n) space for L2 metric. For the problem of enumerating k closest/farthest bichromatic pairs, we shall also discuss the case where we have different numbers of red and blue points. To the authors’ knowledge, no nontrivial algorithms have been known for these problems and our algorithms are faster than trivial ones when k=o(n3/2).

Computing generalized higher-order Voronoi diagrams on triangulated surfaces

2009 ◽  
Vol 215 (1) ◽  
pp. 235-250 ◽  
Author(s):  
Marta Fort ◽  
J. Antoni Sellarès
Keyword(s):  
Voronoi Diagrams ◽  
Higher Order ◽  
Triangulated Surfaces

A semidynamic construction of higher-order voronoi diagrams and its randomized analysis

Algorithmica ◽  
1993 ◽  
Vol 9 (4) ◽  
pp. 329-356 ◽  
Author(s):  
Jean -Daniel Boissonnat ◽  
Olivier Devillers ◽  
Monique Teillaud
Keyword(s):  
Voronoi Diagrams ◽  
Higher Order

scholarly journals A randomized divide and conquer algorithm for higher-order abstract Voronoi diagrams

2016 ◽  
Vol 59 ◽  
pp. 26-38 ◽  
Author(s):  
Cecilia Bohler ◽  
Chih-Hung Liu ◽  
Evanthia Papadopoulou ◽  
Maksym Zavershynskyi
Keyword(s):  
Voronoi Diagrams ◽  
Higher Order ◽  
Divide And Conquer ◽  
Divide And Conquer Algorithm
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