Separator1 (Geometric Separator Problems)
Revision as of 10:29, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Separator1 (Geometric Separator Problems)}} == Description == Given a set $S$ of $n$ possible half-infinite, closed horizontal line segments, is there a non-horizontal separator? Separator definition: Given a set $S$ of $n$ objects in the plane, we call a line $l$ a separator of $S$ if $l$ does not intersect any object in $S$ and both halfplanes bounded by $l$ contain a non-empty subset of the objects in $S$. == Related Problems == Related: Separat...")
Description
Given a set $S$ of $n$ possible half-infinite, closed horizontal line segments, is there a non-horizontal separator?
Separator definition: Given a set $S$ of $n$ objects in the plane, we call a line $l$ a separator of $S$ if $l$ does not intersect any object in $S$ and both halfplanes bounded by $l$ contain a non-empty subset of the objects in $S$.
Related Problems
Related: Separator2
Parameters
n: number of line segments
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| GeomBase | if: to-time $N^{2-\epsilon}$ for some $\epsilon > {0}$ then: from-time: $N^{2-\epsilon'}$ for some $\epsilon' > {0}$ |
1995 | https://doi.org/10.1016/0925-7721(95)00022-2 | link |