Advertisement

Efficient Computation of Time-Dependent Centralities in Air Transportation Networks

  • Annabell Berger
  • Matthias Müller-Hannemann
  • Steffen Rechner
  • Alexander Zock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6552)

Abstract

We introduce indices of centrality to analyze air transportation networks which represent the importance of airports and individual flights dependent on the time of the day (time-dependent centrality indices). Our centrality indices are based on earliest arrival paths with a minimum number of transfers in a time- and event-dependent network model. This means, that all paths correspond to real connections, in particular with transfers which obey minimum transfer times between flights. While the straight-forward computation of these indices is quite expensive, we provide efficient algorithms for the centrality computation. To this end, we construct a certain sequence of pairwise disjoint profile graphs representing all relevant paths by exploiting a special kind of subpath optimality. This avoids unnecessary repeated computations of all optimal time-dependent multi-criteria paths and allows us to use single criterion path queries for the earliest arrival time (without path construction). We have tested our method with original schedule data of 2010 provided by Official Airlines Guide (OAG) on the complete world-wide airport network. Our approach yields a speed-up over the straight-forward centrality computation by a factor of about 100 for the world-wide network.

Keywords

Optimal Path Departure Event Centrality Index Arrival Event Transfer Centrality 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Balcan, D., Colizza, V., Gonçalves, B., Hu, H., Ramasco, J., Verspignani, A.: Multiscale mobility networks and the spatial spreading of infectious diseases. PNAS 106, 21484–21489 (2009)CrossRefGoogle Scholar
  2. 2.
    Colizza, V., Barthélemy, A.B.M., Vespignani, A.: The role of the airline transportation network in the prediction and predictability of global epidemics. PNAS 103, 2015–2020 (2006)CrossRefzbMATHGoogle Scholar
  3. 3.
    Koschützki, D., Lehmann, K.A., Peeters, L., Richter, S., Tenfelde-Podehl, D., Zlotowski, O.: Centrality indices. In: Brandes, U., Erlebach, T. (eds.) Network Analysis. LNCS, vol. 3418, pp. 16–61. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Jacob, R., Koschützki, D., Lehmann, K.A., Peeters, L., Tenfelde-Podehl, D.: Algorithms for centrality indices. In: Brandes, U., Erlebach, T. (eds.) Network Analysis. LNCS, vol. 3418, pp. 62–82. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Borgatti, S., Everett, M.: A graph-theoretic perspective on centrality. Social Networks 28, 466–484 (2006)CrossRefGoogle Scholar
  6. 6.
    Brandes, U.: A faster algorithm for betweenness centrality. Journal of Mathematical Sociology 25, 163–177 (2001)CrossRefzbMATHGoogle Scholar
  7. 7.
    Brandes, U., Pich, C.: Centrality estimation in large networks. I. J. Bifurcation and Chaos 17, 2303–2318 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Geisberger, R., Sanders, P., Schultes, D.: Better approximation of betweenness centrality. In: Munro, J.I., Wagner, D. (eds.) ALENEX, pp. 90–100. SIAM, Philadelphia (2008)Google Scholar
  9. 9.
    Guimerà, R., Amaral, L.: Modeling the world-wide airport network. European Physical Journal B 38, 381–385 (2004)CrossRefGoogle Scholar
  10. 10.
    Guimerà, R., Mossa, S., Turtschi, A., Amaral, L.: The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles. PNAS 102, 7794–7799 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Burghouwt, G., Redondi, R.: Connectivity in air transport networks: models, measures and applications. Technical Report 1/09, Department of Economics and technology Management, University of Bergamo (2009)Google Scholar
  12. 12.
    Malighetti, P., Paleari, S., Redondi, R.: Connectivity of the European airport network: “self-help hubbing” and business implications. Journal of Air Transport Management 14, 53–65 (2008)CrossRefGoogle Scholar
  13. 13.
    Paleari, S., Redondi, R., Malighetti, P.: A comparative study of airport connectivity in China, Europe and US: Which network provides the best service to passengers? Transportation Research Part E: Logistics and Transportation Review 46, 198–210 (2010)CrossRefGoogle Scholar
  14. 14.
    Berger, A., Müller-Hannemann, M.: Subpath-optimality of multi-criteria shortest paths in time-dependent and event-dependent networks. Technical report 2009/1, Martin-Luther-Universität Halle-Wittenberg, Institute of Computer Science (2009)Google Scholar
  15. 15.
    Brodal, G.S., Jacob, R.: Time-dependent networks as models to achieve fast exact time-table queries. In: Proceedings of the 3rd Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS 2003). Electronic Notes in Theoretical Computer Science, vol. 92. Elsevier, Amsterdam (2004)Google Scholar
  16. 16.
    Pyrga, E., Schulz, F., Wagner, D., Zaroliagis, C.: Efficient models for timetable information in public transportation systems. ACM Journal of Experimental Algorithmics 12 (2007); Article 2.4Google Scholar
  17. 17.
    Cook, K., Hasley, E.: The shortest route through a network with time-dependent internodal transit times. Journal of Mathematical Analysis and Applications 14, 493–498 (1966)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Dreyfus, S.: An appraisal of some shortest-path algorithms. Operations Research 17, 395–412 (1969)CrossRefzbMATHGoogle Scholar
  19. 19.
    Orda, A., Rom, R.: Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. J. ACM 37, 607–625 (1990)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Annabell Berger
    • 1
  • Matthias Müller-Hannemann
    • 1
  • Steffen Rechner
    • 1
  • Alexander Zock
    • 2
  1. 1.Department of Computer ScienceMartin-Luther-University Halle-WittenbergHalleGermany
  2. 2.European Center for Aviation Development ECAD GmbHDarmstadtGermany

Personalised recommendations