Fat Heaps without Regular Counters

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


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.


Tree Reduction Priority Queue Numeral System Element Comparison Tree Inventory 
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  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)MathSciNetCrossRefzbMATHGoogle 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)MathSciNetCrossRefzbMATHGoogle 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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