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Customizable Contraction Hierarchies

  • Julian Dibbelt
  • Ben Strasser
  • Dorothea Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8504)

Abstract

We consider the problem of quickly computing shortest paths in weighted graphs given auxiliary data derived in an expensive preprocessing phase. By adding a fast weight-customization phase, we extend Contraction Hierarchies [12] to support the three-phase workflow introduced by Delling et al. [6]. Our Customizable Contraction Hierarchies use nested dissection orders as suggested in [3]. We provide an in-depth experimental analysis on large road and game maps that clearly shows that Customizable Contraction Hierarchies are a very practicable solution in scenarios where edge weights often change.

Keywords

Priority Queue Query Time Lower Common Ancestor Lower Triangle Elimination Tree 
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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References

  1. 1.
    Bast, H., Delling, D., Goldberg, A.V., Müller–Hannemann, M., Pajor, T., Sanders, P., Wagner, D., Werneck, R.F.: Route planning in transportation networks. In: Technical Report MSR-TR-2014-4. Microsoft Research, Mountain View (2014)Google Scholar
  2. 2.
    Batz, G.V., Geisberger, R., Sanders, P., Vetter, C.: Minimum time-dependent travel times with contraction hierarchies. ACM J. Exp. Algorithmics 18, 1–43 (2013)MathSciNetGoogle Scholar
  3. 3.
    Bauer, R., Columbus, T., Rutter, I., Wagner, D.: Search-space size in contraction hierarchies. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part I. LNCS, vol. 7965, pp. 93–104. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Bodlaender, H.L., Koster, A.M.C.A.: Treewidth computations I. Upper bounds. Inform. and Comput. 208, 259–275 (2010)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Chaudhuri, S., Zaroliagis, C.: Shortest paths in digraphs of small treewidth. Part I: Sequential algorithms. Algorithmica 27, 212–226 (2000)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Delling, D., Goldberg, A.V., Pajor, T., Werneck, R.F.: Customizable route planning. In: Pardalos, P.M., Rebennack, S. (eds.) SEA 2011. LNCS, vol. 6630, pp. 376–387. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Delling, D., Goldberg, A.V., Razenshteyn, I., Werneck, R.F.: Graph partitioning with natural cuts. In: 2011 IEEE International Parallel & Distributed Processing Symposium (IPDPS 2011), pp. 1135–1146. IEEE Computer Society, Los Alamitos (2011)CrossRefGoogle Scholar
  8. 8.
    Delling, D., Goldberg, A.V., Razenshteyn, I., Werneck, R.F.: Exact combinatorial branch-and-bound for graph bisection. In: Bader, D.A., Mutzel, P. (eds.) ALENEX 2012, pp. 30–44. SIAM, Philadelphia (2012)Google Scholar
  9. 9.
    Delling, D., Werneck, R.F.: Faster customization of road networks. In: Bonifaci, V., Demetrescu, C., Marchetti-Spaccamela, A. (eds.) SEA 2013. LNCS, vol. 7933, pp. 30–42. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.): The Shortest Path Problem: Ninth DIMACS Implementation Challenge. American Mathematical Society, Rhode Island (2009)Google Scholar
  11. 11.
    Fulkerson, D.R., Gross, O.A.: Incidence matrices and interval graphs. Pacific J. Math. 15, 835–855 (1965)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Geisberger, R., Sanders, P., Schultes, D., Vetter, C.: Exact routing in large road networks using contraction hierarchies. Transportation Science 46, 388–404 (2012)CrossRefGoogle Scholar
  13. 13.
    George, A.: Nested dissection of a regular finite element mesh. SIAM J. Numer. Anal. 10, 345–363 (1973)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    George, A., Liu, J.W.: A quotient graph model for symmetric factorization. In: Duff, I.S., Stewart, G.W. (eds.) Sparse Matrix Proceedings, pp. 154–175. SIAM, Philadelphia (1978)Google Scholar
  15. 15.
    Holzer, M., Schulz, F., Wagner, D.: Engineering multilevel overlay graphs for shortest-path queries. ACM J. Exp. Algorithmics 13, 1–26 (2008)MathSciNetGoogle Scholar
  16. 16.
    Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20, 359–392 (1999)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Lipton, R.J., Rose, D.J., Tarjan, R.: Generalized nested dissection. SIAM J. Numer. Anal. 16, 346–358 (1979)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Planken, L., de Weerdt, M., van Krogt, R.: Computing all-pairs shortest paths by leveraging low treewidth. J. Artificial Intelligence Res. 43, 353–388 (2012)MATHMathSciNetGoogle Scholar
  19. 19.
    Sanders, P., Schulz, C.: Think locally, act globally: Highly balanced graph partitioning. In: Bonifaci, V., Demetrescu, C., Marchetti-Spaccamela, A. (eds.) SEA 2013. LNCS, vol. 7933, pp. 164–175. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. 20.
    Schulz, F., Wagner, D., Weihe, K.: Dijkstra’s algorithm on-line: An empirical case study from public railroad transport. ACM J. Exp. Algorithmics 5, 1–23 (2000)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Storandt, S.: Contraction hierarchies on grid graphs. In: Timm, I.J., Thimm, M. (eds.) KI 2013. LNCS, vol. 8077, pp. 236–247. Springer, Heidelberg (2013)Google Scholar
  22. 22.
    Sturtevant, N.: Benchmarks for grid-based pathfinding. Transactions on Computational Intelligence and AI in Games (2012)Google Scholar
  23. 23.
    Zeitz, T.: Weak contraction hierarchies work! Bachelor thesis. KIT, Karlsruhe (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Julian Dibbelt
    • 1
  • Ben Strasser
    • 1
  • Dorothea Wagner
    • 1
  1. 1.Karlsruhe Institute of Technology (KIT)KarlsruheGermany

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