A practical algorithm for 3-admissibility

TL;DR

This paper introduces the first explicit, practical algorithm to determine the 3-admissibility of graphs efficiently, demonstrating its applicability on real-world networks and revealing insights about their structural properties.

Contribution

The paper presents a novel, efficient algorithm for computing 3-admissibility, with experimental validation on real-world networks showing its practicality and surprising structural findings.

Findings

Most real-world networks have 3-admissibility close to their 2-admissibility.

The proposed algorithm operates in linear time and space relative to input size.

3-admissibility is a useful measure for understanding network structure.

Abstract

The $3$-admissibility of a graph is a promising measure to identify real-world networks that have an algorithmically favourable structure. We design an algorithm that decides whether the $3$-admissibility of an input graph~$G$ is at most~$p$ in time~\runtime and space~\memory, where $m$ is the number of edges in $G$ and $n$ the number of vertices. To the best of our knowledge, this is the first explicit algorithm to compute the $3$-admissibility. The linear dependence on the input size in both time and space complexity, coupled with an `optimistic' design philosophy for the algorithm itself, makes this algorithm practicable, as we demonstrate with an experimental evaluation on a corpus of \corpussize real-world networks. Our experimental results show, surprisingly, that the $3$-admissibility of most real-world networks is not much larger than the $2$-admissibility, despite the fact that the former has better algorithmic properties than the latter.