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On the Solvability of the Six Degrees of Kevin Bacon Game

A Faster Graph Diameter and Radius Computation Method
  • Michele Borassi
  • Pierluigi Crescenzi
  • Michel Habib
  • Walter Kosters
  • Andrea Marino
  • Frank Takes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8496)

Abstract

In this paper, we will propose a new algorithm that computes the radius and the diameter of a graph G = (V,E), by finding bounds through heuristics and improving them until exact values can be guaranteed. Although the worst-case running time is \(\mathcal{O}(|V|\cdot |E|)\), we will experimentally show that, in the case of real-world networks, it performs much better, finding the correct radius and diameter value after 10–100 BFSes instead of |V| BFSes (independent of the value of |V|), and thus having running time \(\mathcal{O}(|E|)\). Apart from efficiency, compared to other similar methods, the one proposed in this paper has three other advantages. It is more robust (even in the worst cases, the number of BFSes performed is not very high), it is able to simultaneously compute radius and diameter (halving the total running time whenever both values are needed), and it works both on directed and undirected graphs with very few modifications. As an application example, we use our new algorithm in order to determine the solvability over time of the “six degrees of Kevin Bacon” game.

Keywords

Undirected Graph Closeness Centrality Central Vertex Actor Graph Graph Diameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Michele Borassi
    • 1
  • Pierluigi Crescenzi
    • 2
  • Michel Habib
    • 3
  • Walter Kosters
    • 4
  • Andrea Marino
    • 5
  • Frank Takes
    • 4
  1. 1.IMT Institute of Advanced StudiesLuccaItaly
  2. 2.Dipartimento di Sistemi e InformaticaUniversità di FirenzeItaly
  3. 3.LIAFAUMR 7089 CNRS & Université Paris DiderotParis 7France
  4. 4.Leiden Institute of Advanced Computer ScienceLeiden UniversityThe Netherlands
  5. 5.Dipartimento di InformaticaUniversità di MilanoItaly

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