Tabulation of Noncrossing Acyclic Digraphs

Marco Kuhlmann

Tabulation of Noncrossing Acyclic Digraphs

Data Structures and Algorithms 2015-04-21 v1 Combinatorics

Authors: Marco Kuhlmann

Abstract

I present an algorithm that, given a number $n \geq 1$ , computes a compact representation of the set of all noncrossing acyclic digraphs with $n$ nodes. This compact representation can be used as the basis for a wide range of dynamic programming algorithms on these graphs. As an illustration, along with this note I am releasing the implementation of an algorithm for counting the number of noncrossing acyclic digraphs of a given size. The same tabulation can be modified to count other classes of combinatorial structures, including weakly connected noncrossing acyclic digraphs, general noncrossing digraphs, noncrossing undirected graphs.

Keywords

graph theory graph algorithms planar graph drawing

Cite

@article{arxiv.1504.04993,
  title  = {Tabulation of Noncrossing Acyclic Digraphs},
  author = {Marco Kuhlmann},
  journal= {arXiv preprint arXiv:1504.04993},
  year   = {2015}
}