Fat Heaps without Regular Counters

  • Amr Elmasry
  • Jyrki Katajainen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7157)

Abstract

We introduce a variant of fat heaps that does not rely on regular counters, and still achieves the optimal worst-case bounds: O(1) for find-min, insert and decrease, and \(O(\lg n)\) for delete and delete-min. Our variant is simpler to explain, more efficient, and easier to implement. Experimental results suggest that our implementation is superior to structures, like run-relaxed heaps, that achieve the same worst-case bounds, and competitive to structures, like Fibonacci heaps, that achieve the same bounds in the amortized sense.

Keywords

Tree Reduction Priority Queue Numeral System Element Comparison Tree Inventory 
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.
    Brodal, G.S.: Fast Meldable Priority Queues. In: Sack, J.-R., Akl, S.G., Dehne, F., Santoro, N. (eds.) WADS 1995. LNCS, vol. 955, pp. 282–290. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  2. 2.
    Brodal, G.S.: Worst-case efficient priority queues. In: 7th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 52–58. ACM/SIAM, New York/Philadelphia (1996)Google Scholar
  3. 3.
    Brown, M.R.: Implementation and analysis of binomial queue algorithms. SIAM Journal on Computing 7(3), 298–319 (1978)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    Clancy, M.J., Knuth, D.E.: A programming and problem-solving seminar. Technical Report STAN-CS-77-606, Stanford University (1977)Google Scholar
  6. 6.
    Driscoll, J.R., Gabow, H.N., Shrairman, R., Tarjan, R.E.: Relaxed heaps: An alternative to Fibonacci heaps with applications to parallel computation. Communications of the ACM 31(11), 1343–1354 (1988)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Elmasry, A., Jensen, C., Katajainen, J.: Relaxed weak queues: An alternative to run-relaxed heaps. CPH STL Report 2005-2, Department of Computer Science, University of Copenhagen (2005)Google Scholar
  8. 8.
    Elmasry, A., Jensen, C., Katajainen, J.: Multipartite priority queues. ACM Transactions on Algorithms 5(1), 14:1–14:19 (2008)Google Scholar
  9. 9.
    Elmasry, A., Jensen, C., Katajainen, J.: Strictly-Regular Number System and Data Structures. In: Kaplan, H. (ed.) SWAT 2010. LNCS, vol. 6139, pp. 26–37. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM 34(3), 596–615 (1987)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Guibas, L.J., McCreight, E.M., Plass, M.F., Roberts, J.R.: A new representation for linear lists. In: 9th Annual ACM Symposium on Theory of Computing, pp. 49–60. ACM, New York (1977)Google Scholar
  12. 12.
    Kaplan, H., Shafrir, N., Tarjan, R.E.: Meldable heaps and Boolean union-find. In: 34th Annual ACM Symposium on Theory of Computing, pp. 573–582. ACM, New York (2002)Google Scholar
  13. 13.
    Kaplan, H., Tarjan, R.E.: New heap data structures. Technical Report TR-597-99, Department of Computer Science, Princeton University (1999)Google Scholar
  14. 14.
    Vuillemin, J.: A data structure for manipulating priority queues. Communications of the ACM 21(4), 309–315 (1978)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Williams, J.W.J.: Algorithm 232: Heapsort. Communications of the ACM 7(6), 347–348 (1964)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Amr Elmasry
    • 1
  • Jyrki Katajainen
    • 1
  1. 1.Department of Computer ScienceUniversity of CopenhagenDenmark

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