Description
Given a set of n red and n blue points in the plane, we are interested
in matching red points with blue points by straight line segments so
that the segments do not cross. We develop a range of tools for dealing
with the non-crossing matchings of points in convex position. It turns
out that the points naturally partition into groups that we refer to as
orbits, with a number of properties that prove useful for studying and
efficiently processing the non-crossing matchings.
Bottleneck matching is such a matching that minimizes the length of the
longest segment. Illustrating the use of the developed tools, we show
how to solve the problem of finding bottleneck matchings of points in
convex position faster than before.
Joint work with Marko Savić.