A QPTAS for the Base of the Number of Triangulations of a Planar Point Set

Abstract: The number of triangulations of a planar n point set is known to be $c^n$, where the base $c$ lies between $2.43$ and $30.$ The fastest known algorithm for counting triangulations of a planar n point set runs in $O^*(2^n)$ time. The fastest known arbitrarily close approximation algorithm for the base of the number of triangulations of a planar n point set runs in time subexponential in $n.$ We present the first quasi-polynomial approximation scheme for the base of the number of triangulations of a planar point set.