1 research outputs found
Point sets with many non-crossing matchings
The maximum number of non-crossing straight-line perfect matchings that a set
of points in the plane can have is known to be and
. The lower bound, due to Garc\'ia, Noy, and Tejel (2000) is
attained by the double chain, which has such matchings.
We reprove this bound in a simplified way that uses the novel notion of
down-free matching, and apply this approach on several other constructions. As
a result, we improve the lower bound. First we show that double zigzag chain
with points has such matchings with . Next we analyze further generalizations of double zigzag chains -
double -chains. The best choice of parameters leads to a construction with
matchings, with . The derivation of this
bound requires an analysis of a coupled dynamic-programming recursion between
two infinite vectors.Comment: 33 pages, 19 figures, 2 table