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A Practical Algorithm for 2-Admissibility

Authors Christine Awofeso , Patrick Greaves , Oded Lachish , Felix Reidl

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  • Theory of computation → Graph algorithms analysis
Keywords
  • Sparse graphs
  • admissibility

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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(p⁴ |V(G)|) and space O(|E(G)| + p²). 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.

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Christine Awofeso, Patrick Greaves, Oded Lachish, and Felix Reidl. A Practical Algorithm for 2-Admissibility. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SEA.2025.3

Author Details

Christine Awofeso
  • Birkbeck, University of London, UK
Patrick Greaves
  • Birkbeck, University of London, UK
Oded Lachish
  • Birkbeck, University of London, UK
Felix Reidl
  • Birkbeck, University of London, UK

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References

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