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CCCG
2008
13 years 7 months ago
Smallest enclosing circle centered on a query line segment
Given a set of n points P = {p1, p2, . . . , pn} in the plane, we show how to preprocess P such that for any query line segment L we can report in O(log n) time the smallest enclo...
Prosenjit Bose, Stefan Langerman, Sasanka Roy
JCT
2011
89views more  JCT 2011»
13 years 16 days ago
On lines, joints, and incidences in three dimensions
We extend (and somewhat simplify) the algebraic proof technique of Guth and Katz [7], to obtain several sharp bounds on the number of incidences between lines and points in three ...
György Elekes, Haim Kaplan, Micha Sharir
COMPGEOM
1992
ACM
13 years 9 months ago
On-Line Steiner Trees in the Euclidean Plane
Suppose we are given a sequence of n points in the Euclidean plane, and our objective is to construct, on-line, a connected graph that connects all of them, trying to minimize the...
Noga Alon, Yossi Azar
ENDM
2008
81views more  ENDM 2008»
13 years 5 months ago
The maximum number of halving lines and the rectilinear crossing number of Kn for n
For n 27 we present exact values for the maximum number h(n) of halving lines and h(n) of halving pseudolines, determined by n points in the plane. For this range of values of n ...
Bernardo M. Ábrego, Silvia Fernández...
CIAC
2006
Springer
278views Algorithms» more  CIAC 2006»
13 years 9 months ago
Covering a Set of Points with a Minimum Number of Lines
We consider the minimum line covering problem: given a set S of n points in the plane, we want to find the smallest number l of straight lines needed to cover all n points in S. W...
Magdalene Grantson, Christos Levcopoulos