scholarly journals Ray Shooting and Parametric Search

1993 ◽  
Vol 22 (4) ◽  
pp. 794-806 ◽  
Author(s):  
Pankaj K. Agarwal ◽  
Jiří Matoušek
2010 ◽  
Vol 7 (1) ◽  
pp. 3-19
Author(s):  
Stéphane Mancini ◽  
Zahir Larabi ◽  
Yves Mathieu ◽  
Tomasz Toczek ◽  
Lionel Pierrefeu

Author(s):  
Joachim Gudmundsson ◽  
Sampson Wong

The yolk is an important concept in spatial voting games: the yolk center generalises the equilibrium and the yolk radius bounds the uncovered set. We present near-linear time algorithms for computing the yolk in the plane. To the best of our knowledge our algorithm is the first that does not precompute median lines, and hence is able to break the best known upper bound of O(n4/3) on the number of limiting median lines. We avoid this requirement by carefully applying Megiddo’s parametric search technique, which is a powerful framework that could lead to faster algorithms for other spatial voting problems.


2008 ◽  
Vol 41 (1-2) ◽  
pp. 68-76 ◽  
Author(s):  
Boris Aronov ◽  
Mark de Berg ◽  
Chris Gray

1999 ◽  
Vol 35 (21) ◽  
pp. 1804 ◽  
Author(s):  
F. Villanese ◽  
W.G. Scanlon ◽  
N.E. Evans ◽  
E. Gambi

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