An Almost Optimal Algorithm for Voronoi Diagrams of Non-disjoint Line Segments

2015 ◽  
pp. 125-136
Author(s):  
Sang Won Bae
Keyword(s):  
Optimal Algorithm ◽  
Voronoi Diagrams ◽  
Line Segments ◽  
Disjoint Line

OPTIMAL BINARY SPACE PARTITIONS FOR SEGMENTS IN THE PLANE

2012 ◽  
Vol 22 (03) ◽  
pp. 187-205 ◽  
Author(s):  
MARK DE BERG ◽  
AMIRALI KHOSRAVI
Keyword(s):  
Recursive Partitioning ◽  
Np Hard ◽  
Line Segments ◽  
Minimum Number ◽  
Disjoint Line

An optimal BSP for a set S of disjoint line segments in the plane is a BSP for S that produces the minimum number of cuts. We study optimal BSPs for three classes of BSPs, which differ in the splitting lines that can be used when partitioning a set of fragments in the recursive partitioning process: free BSPs can use any splitting line, restricted BSPs can only use splitting lines through pairs of fragment endpoints, and auto-partitions can only use splitting lines containing a fragment. We obtain the following two results: • It is NP-hard to decide whether a given set of segments admits an auto-partition that does not make any cuts. • An optimal restricted BSP makes at most 2 times as many cuts as an optimal free BSP for the same set of segments.

scholarly journals Every Set of Disjoint Line Segments Admits a Binary Tree

2001 ◽  
Vol 26 (3) ◽  
pp. 387-410 ◽  
Author(s):  
P. Bose ◽  
M. E. Houle ◽  
G. T. Toussaint
Keyword(s):  
Binary Tree ◽  
Line Segments ◽  
Disjoint Line

scholarly journals An optimal algorithm for intersecting line segments in the plane

1992 ◽  
Vol 39 (1) ◽  
pp. 1-54 ◽  
Author(s):  
Bernard Chazelle ◽  
Herbert Edelsbrunner
Keyword(s):  
Optimal Algorithm ◽  
Line Segments

scholarly journals Alternating paths through disjoint line segments

2003 ◽  
Vol 87 (6) ◽  
pp. 287-294 ◽  
Author(s):  
Michael Hoffmann ◽  
Csaba D Tóth
Keyword(s):  
Line Segments ◽  
Disjoint Line
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