2015/04/20 by Kuhlmann, Marco
#Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1504.04993
I present an algorithm that, given a number n ≥ 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.