Counting and enumerating crossing-free geometric graphs

Abstract

We describe a framework for constructing data structures which allow fast counting and enumeration of various types of crossing-free geometric graphs on a planar point set. The framework generalizes ideas of Alvarez and Seidel, who used them to count triangulations in time $O(2^nn^2)$ where $n$ is the number of points. The main idea is to represent geometric graphs as source-sink paths in a directed acyclic graph.