Improving the Cache-Efficiency of Shortest Path Search

  • Stefan Edelkamp
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10505)


Flood-filling algorithms as used for coloring images and shadow casting show that improved locality greatly increases the cache performance and, in turn, reduces the running time of an algorithm. In this paper we look at Dijkstra’s method to compute the shortest paths for example to generate pattern databases. As cache-improving contributions, we propose edge-cost factorization and flood-filling the memory layout of the graph. We conduct experiments in commercial game maps and compare the new priority queues with advanced heap implementations as well as and with alternative bucket implementations.


  1. 1.
    Ahuja, R.K., Mehlhorn, K., Orlin, J.B., Tarjan, R.E.: Faster algorithms for the shortest path problem. J. ACM 37(2), 213–223 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Brodal, G.S.: Worst-case efficient priority queues. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 52–58 (1996)Google Scholar
  3. 3.
    Bruun, A., Edelkamp, S., Katajainen, J., Rasmussen, J.: Policy-based benchmarking of weak heaps and their relatives. In: Festa, P. (ed.) SEA 2010. LNCS, vol. 6049, pp. 424–435. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-13193-6_36 CrossRefGoogle Scholar
  4. 4.
    Culberson, J.C., Schaeffer, J.: Pattern databases. Comput. Intell. 14(4), 318–334 (1998)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dial, R.B.: Shortest-path forest with topological ordering. Commun. ACM 12(11), 632–633 (1969)CrossRefGoogle Scholar
  6. 6.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Driscoll, J.R., Gabow, H.N., Shrairman, R., Tarjan, R.E.: Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation. Commun. ACM 31(11), 1343–1354 (1988)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Edelkamp, S.: Planning with pattern databases. In: ECP, pp. 13–24 (2001)Google Scholar
  9. 9.
    Edelkamp, S., Schrödl, S.: Localizing A*. In: AAAI, pp. 885–890 (2000)Google Scholar
  10. 10.
    Evangelista, S., Kristensen, L.M.: A sweep-line method for Büchi automata-based model checking. Fundam. Inform. 131(1), 27–53 (2014)zbMATHGoogle Scholar
  11. 11.
    Floyd, R.W.: Algorithm 245: treesort 3. Commun. ACM 7(12), 701 (1964)CrossRefGoogle Scholar
  12. 12.
    Fredman, M.L., Sedgewick, R., Sleator, D.D., Tarjan, R.E.: The pairing heap: a new form of self-adjusting heap. Algorithmica 1(1), 111–129 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithm. J. ACM 34(3), 596–615 (1987)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Geisberger, R., Schieferdecker, D.: Heuristic contraction hierarchies with approximation guarantee. In: SOCS, pp. 31–38 (2010)Google Scholar
  15. 15.
    Ghiani, G., Guerriero, F., Laporte, G., Musmanno, R.: Real-time vehicle routing: solution concepts, algorithms and parallel computing strategies. Eur. J. Oper. Res. 151, 1–11 (2003)CrossRefzbMATHGoogle Scholar
  16. 16.
    Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for heuristic determination of minimum path cost. IEEE Trans. Syst. Sci. Cybern. 4, 100–107 (1968)CrossRefGoogle Scholar
  17. 17.
    Horowitz, E., Sahni, S., Anderson-Freed, S.: Fundamentals of Data Structures in C, 2nd edn. Silicon Press, Summit (2007)zbMATHGoogle Scholar
  18. 18.
    Kaplan, H., Tarjan, R.E., Zwick, U.: Fibonacci heaps revisited, pp. 187–205 (2014). arXiv:1407.5750v1
  19. 19.
    Klein, P., Rao, S., Rauch, M., Subramanian, S.: Faster shortest-path algorithms for planar graphs. J. Comput. Syst. Sci. 55(1), 3–23 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Korf, R.E.: Finding optimal solutions to Rubik’s Cube using pattern databases. In: AAAI, pp. 700–705 (1997)Google Scholar
  21. 21.
    Kristensen, L., Mailund, T.: Path finding with the sweep-line method using external storage. In: ICFEM, pp. 319–337 (2003)Google Scholar
  22. 22.
    LaMarca, A., Ladner, R.E.: The influence of caches on the performance of sorting. J. Algorithms 31(1), 66–104 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Liebana, D.P., Powley, E.J., Whitehouse, D., Rohlfshagen, P., Samothrakis, S., Cowling, P.I., Lucas, S.M.: Solving the physical traveling salesman problem: tree search and macro actions. IEEE Trans. Comput. Intell. AI Games 6(1), 31–45 (2014)CrossRefGoogle Scholar
  24. 24.
    Lieberman, H.: How to color in a coloring book. SIGGRAPH Comput. Graph. 12(3), 111–116 (1978)CrossRefGoogle Scholar
  25. 25.
    Otte, M.: On solving floating point SSSP using an integer priority queue. CoRR, abs/1606.00726 (2016)Google Scholar
  26. 26.
    Sanders, P.: Fast priority queues for cached memory. ACM J. Exp. Algorithmics 5, 7 (2000)CrossRefzbMATHGoogle Scholar
  27. 27.
    Stasko, J.T., Vitter, J.S.: Pairing heaps: experiments and analysis. Commun. ACM 30(3), 234–249 (1987)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Sturtevant, N.R.: The grid-based path planning competition. AI Mag. 35(3), 66–69 (2014)CrossRefGoogle Scholar
  29. 29.
    Thorup, M.: Undirected single-source shortest paths with positive integer weights in linear time. J. ACM 46, 362–394 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Wagner, D., Willhalm, T.: Geometric speed-up techniques for finding shortest paths in large sparse graphs. In: Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 776–787. Springer, Heidelberg (2003). doi: 10.1007/978-3-540-39658-1_69 CrossRefGoogle Scholar
  31. 31.
    Williams, J.W.J.: Algorithm 232: heapsort. Commun. ACM 7(6), 347–348 (1964)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.King’s College LondonLondonUK

Personalised recommendations