Title
Extremal point queries with lines and line segments and related problems
Abstract
We address a number of extremal point query problems when P is a set of n points in R^d, d=3 a constant, including the computation of the farthest point from a query line and the computation of the farthest point from each of the lines spanned by the points in P. In R^3, we give a data structure of size O(n^1^+^@?), that can be constructed in O(n^1^+^@?) time and can report the farthest point of P from a query line segment in O(n^2^/^3^+^@?) time, where @?0 is an arbitrarily small constant. Applications of our results also include: (1) Sub-cubic time algorithms for fitting a polygonal chain through an indexed set of points in R^d, d=3 a constant, and (2) A sub-quadratic time and space algorithm that, given P and an anchor point q, computes the minimum (maximum) area triangle defined by q with P@?{q}.
Year
DOI
Venue
2005
10.1016/j.comgeo.2005.03.002
Comput. Geom.
Keywords
Field
DocType
area triangle,query,farthest point,computational geometry,algorithm,sub-cubic time algorithm,query line segment,extremal point query problem,size o,n point,query line,segment,related problem,anchor point q,sub-quadratic time,data structure,extreme point,indexation
Discrete mathematics,Line segment,Data structure,Combinatorics,Spacetime,Computational geometry,Polygonal chain,Mathematics,Computation
Journal
Volume
Issue
ISSN
32
3
Computational Geometry: Theory and Applications
Citations 
PageRank 
References 
3
0.50
25
Authors
2
Name
Order
Citations
PageRank
Ovidiu Daescu127645.78
Robert Serfling2223.80