1 research outputs found
On Triangluar Separation of Bichromatic Point Sets in Polygonal Environment
Let be a simple polygonal environment with vertices in the
plane. Assume that a set of blue points and a set of red points
are distributed in . We study the problem of computing triangles
that separate the sets and , and fall in . We call these
triangles \emph{inscribed triangular separators}. We propose an
output-sensitive algorithm to solve this problem in time, where is the size of convex hull of ,
and is the number of inscribed triangular separators. We also
study the case where there does not exist any inscribed triangular separators.
This may happen due to the tight distribution of red points around convex hull
of while no red points are inside this hull. In this case we focus to
compute a triangle that separates most of the blue points from the red points.
We refer to these triangles as \emph{maximum triangular separators}. Assuming
, we design a constant-factor approximation algorithm to compute such a
separator in time. "Eligible for best student paper