Strictly Implicit Priority Queues: On the Number of Moves and Worst-Case Time

  • Gerth Stølting Brodal
  • Jesper Sindahl NielsenEmail author
  • Jakob Truelsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9214)


The binary heap of Williams (1964) is a simple priority queue characterized by only storing an array containing the elements and the number of elements n – here denoted a strictly implicit priority queue. We introduce two new strictly implicit priority queues. The first structure supports amortized O(1) time Insert and \(O(\log n)\) time ExtractMin operations, where both operations require amortized O(1) element moves. No previous implicit heap with O(1) time Insert supports both operations with O(1) moves. The second structure supports worst-case O(1) time Insert and \(O(\log n)\) time (and moves) ExtractMin operations. Previous results were either amortized or needed \(O(\log n)\) bits of additional state information between operations.


Minimum Element Priority Queue Single Structure Empty Slot Binomial 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Brodal, G.S.: A survey on priority queues. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds.) Ianfest-66. LNCS, vol. 8066, pp. 150–163. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  2. 2.
    Brodal, G.S., Fagerberg, R., Jacob, R.: Cache oblivious search trees via binary trees of small height. In: Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 39–48 (2002)Google Scholar
  3. 3.
    Brodal, G.S., Nielsen, J.S., Truelsen, J.: Finger search in the implicit model. In: Chao, K.-M., Hsu, T.-S., Lee, D.-T. (eds.) ISAAC 2012. LNCS, vol. 7676, pp. 527–536. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  4. 4.
    Brodal, G.S., Nielsen, J.S., Truelsen, J.: Strictly implicit priority queues: On the number of moves and worst-case time (2015). CoRR, abs/1505.00147Google Scholar
  5. 5.
    Carlsson, S., Munro, J.I., Poblete, P.V.: An implicit binomial queue with constant insertion time. In: Karlsson, R., Lingas, A. (eds.) SWAT 88. LNCS, vol. 318, pp. 1–13. Springer, Heidelberg (1988) CrossRefGoogle Scholar
  6. 6.
    Carlsson, S., Sundström, M.: Linear-time in-place selection in less than 3n. In: Staples, J., Katoh, N., Eades, P., Moffat, A. (eds.) ISAAC 1995. LNCS, vol. 1004, pp. 244–253. Springer, Heidelberg (1995) CrossRefGoogle Scholar
  7. 7.
    Edelkamp, S., Elmasry, A., Katajainen, J.: Ultimate binary heaps, Manuscript (2013)Google Scholar
  8. 8.
    Franceschini, G.: Sorting stably, in place, with \(O(n \log n)\) comparisons and \(O(n)\) moves. Theory of Computing Systems 40(4), 327–353 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Franceschini, G., Munro, J.I.: Implicit dictionaries with \(O(1)\) modifications per update and fast search. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 404–413 (2006)Google Scholar
  10. 10.
    Johnson, D.B.: Efficient algorithms for shortest paths in sparse networks. Journal of the ACM 24(1), 1–13 (1977)CrossRefzbMATHGoogle Scholar
  11. 11.
    Harvey, N.J.A., Zatloukal, K.C.: The post-order heap. In: 3rd International Conference on Fun with Algorithms (2004)Google Scholar
  12. 12.
    Williams, J.W.J.: Algorithm 232: Heapsort. Communications of the ACM 7(6), 347–348 (1964)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  • Jesper Sindahl Nielsen
    • 1
    Email author
  • Jakob Truelsen
    • 1
  1. 1.MADALGO, Department of Computer ScienceAarhus UniversityAarhusDenmark

Personalised recommendations