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: 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