Strictly-Regular Number System and Data Structures

  • Amr Elmasry
  • Claus Jensen
  • Jyrki Katajainen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6139)


We introduce a new number system that we call the strictly-regular system, which efficiently supports the operations: digit-increment, digit-decrement, cut, concatenate, and add. Compared to other number systems, the strictly-regular system has distinguishable properties. It is superior to the regular system for its efficient support to decrements, and superior to the extended-regular system for being more compact by using three symbols instead of four. To demonstrate the applicability of the new number system, we modify Brodal’s meldable priority queues making deletion require at most \(2\lg{n}+O(1)\) element comparisons (improving the bound from \(7 \lg{n} + O(1)\)) while maintaining the efficiency and the asymptotic time bounds for all operations.


Number System Priority Queue Current Node Regular System Valid Sequence 
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.
    Clancy, M., Knuth, D.: A programming and problem-solving seminar. Technical Report STAN-CS-77-606, Dept. of Computer Science, Stanford University (1977)Google Scholar
  2. 2.
    Guibas, L.J., McCreight, E.M., Plass, M.F., Roberts, J.R.: A new representation for linear lists. In: Proceedings of the 9th Annual ACM Symposium on Theory of Computing, pp. 49–60. ACM Press, New York (1977)Google Scholar
  3. 3.
    Vuillemin, J.: A data structure for manipulating priority queues. Communications of the ACM 21(4), 309–315 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Okasaki, C.: Purely Functional Data Structures. Cambridge University Press, Cambridge (1998)CrossRefGoogle Scholar
  5. 5.
    Aho, A.V., Lam, M.S., Sethi, R., Ullman, J.D.: Compilers: Principles, Techniques, & Tools, 2nd edn. Pearson Education, Inc., London (2007)Google Scholar
  6. 6.
    Kaplan, H., Shafrir, N., Tarjan, R.E.: Meldable heaps and Boolean union-find. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing, pp. 573–582. ACM Press, New York (2002)Google Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    Brodal, G.S.: Worst-case efficient priority queues. In: Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 52–58. ACM/SIAM (1996)Google Scholar
  9. 9.
    Kaplan, H., Tarjan, R.E.: Purely functional representations of catenable sorted lists. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 202–211. ACM, New York (1996)Google Scholar
  10. 10.
    Elmasry, A.: A priority queue with the working-set property. International Journal of Foundations of Computer Science 17(6), 1455–1465 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Elmasry, A., Jensen, C., Katajainen, J.: Two-tier relaxed heaps. Acta Informatica 45(3), 193–210 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Elmasry, A., Jensen, C., Katajainen, J.: Multipartite priority queues. ACM Transactions on Algorithms, Article 14 5(1) (2008)Google Scholar
  13. 13.
    Jensen, C.: A note on meldable heaps relying on data-structural bootstrapping. CPH STL Report 2009-2, Department of Computer Science, University of Copenhagen (2009),
  14. 14.
    Kaplan, H., Tarjan, R.E.: Persistent lists with catenation via recursive slow-down. In: Proceedings of the 27th Annual ACM Symposium on Theory of Computing, pp. 93–102. ACM, New York (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Amr Elmasry
    • 1
  • Claus Jensen
    • 2
  • Jyrki Katajainen
    • 3
  1. 1.Max-Planck Institut für InformatikSaarbrückenGermany
  2. 2.The Royal LibraryCopenhagenDenmark
  3. 3.Department of Computer ScienceUniversity of CopenhagenDenmark

Personalised recommendations