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Algorithmica

, Volume 81, Issue 4, pp 1535–1560 | Cite as

A Polynomial-Time Algorithm for Detecting the Possibility of Braess Paradox in Directed Graphs

  • Pietro Cenciarelli
  • Daniele GorlaEmail author
  • Ivano Salvo
Article

Abstract

A directed multigraph is said vulnerable if it can generate Braess paradox in traffic networks. In this paper, we give a graph–theoretic characterisation of vulnerable directed multigraphs. Analogous results appeared in the literature only for undirected multigraphs and for a specific family of directed multigraphs. The proof of our characterisation provides the first polynomial time algorithm that checks if a general directed multigraph is vulnerable in \(\mathcal{O}(|V| \cdot |E|^2)\). Our algorithm also contributes to the directed subgraph homeomorphism problem without node mapping, by providing another pattern graph for which a polynomial time algorithm exists.

Keywords

Braess paradox Traffic networks Graph theory Graph algorithms Subgraph homeomorphism 

Notes

Acknowledgements

We are very grateful to the anonymous referees, whose careful reading has radically improved a preliminary version of this work.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceSapienza University of RomeRomeItaly

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