A practical algorithm for 2-admissibility

TL;DR

This paper introduces a practical, polynomial-time algorithm to determine the 2-admissibility of graphs, enabling analysis of large real-world networks with efficiency and low memory usage.

Contribution

The paper presents the first practical implementation of an algorithm to compute 2-admissibility, demonstrating its efficiency on large real-world networks.

Findings

Algorithm runs efficiently on networks with millions of edges.

Many real-world networks have small 2-admissibility.

The implementation has a low memory footprint.

Abstract

The $2$-admissibility of a graph is a promising measure to identify real-world networks which have an algorithmically favourable structure. In contrast to other related measures, like the weak/strong $2$-colouring numbers or the maximum density of graphs that appear as $1$-subdivisions, the $2$-admissibility can be computed in polynomial time. However, so far these results are theoretical only and no practical implementation to compute the $2$-admissibility exists. Here we present an algorithm which decides whether the $2$-admissibility of an input graph $G$ is at most $p$ in time $O(p^4 |V(G)|)$ and space $O(|E(G)| + p^2)$. The simple structure of the algorithm makes it easy to implement. We evaluate our implementation on a corpus of 214 real-world networks and find that the algorithm runs efficiently even on networks with millions of edges, that it has a low memory footprint, and that indeed many networks have a small $2$-admissibility.