Tabulation of Noncrossing Acyclic Digraphs

• Main Author: Kuhlmann, Marco
• Format: Journal Article
• Language: English
• Published: 20-04-2015
• Subjects: Computer Science - Data Structures and Algorithms; Mathematics - Combinatorics
• DOI: 10.48550/arxiv.1504.04993

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.