Document Open Access Logo

Fast Dynamic Arrays

Authors Philip Bille, Anders Roy Christiansen, Mikko Berggren Ettienne, Inge Li Gørtz

Thumbnail PDF


  • Filesize: 0.62 MB
  • 13 pages

Document Identifiers

Author Details

Philip Bille
Anders Roy Christiansen
Mikko Berggren Ettienne
Inge Li Gørtz

Cite AsGet BibTex

Philip Bille, Anders Roy Christiansen, Mikko Berggren Ettienne, and Inge Li Gørtz. Fast Dynamic Arrays. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 16:1-16:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


We present a highly optimized implementation of tiered vectors, a data structure for maintaining a sequence of n elements supporting access in time O(1) and insertion and deletion in time O(n^e) for e > 0 while using o(n) extra space. We consider several different implementation optimizations in C++ and compare their performance to that of vector and set from the standard library on sequences with up to 10^8 elements. Our fastest implementation uses much less space than set while providing speedups of 40x for access operations compared to set and speedups of 10.000x compared to vector for insertion and deletion operations while being competitive with both data structures for all other operations.
  • Dynamic Arrays
  • Tiered Vectors


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Andrej Brodnik, Svante Carlsson, Erik D. Demaine, J. Ian Munro, and Robert Sedgewick. Resizable arrays in optimal time and space. In Proceedings of the 6th International Workshop on Algorithms and Data Structures, WADS'99, pages 37-48, London, UK, UK, 1999. Springer-Verlag. URL:
  2. Paul F. Dietz. Optimal algorithms for list indexing and subset rank. In Proceedings of the Workshop on Algorithms and Data Structures, WADS'89, pages 39-46, London, UK, UK, 1989. Springer-Verlag. URL:
  3. Greg N. Frederickson. Implicit data structures for the dictionary problem. J. ACM, 30(1):80-94, January 1983. URL:
  4. M. Fredman and M. Saks. The cell probe complexity of dynamic data structures. In Proceedings of the Twenty-first Annual ACM Symposium on Theory of Computing, STOC'89, pages 345-354, New York, NY, USA, 1989. ACM. URL:
  5. Michael T. Goodrich and John G. Kloss. Tiered vectors: Efficient dynamic arrays for rank-based sequences. In Frank Dehne, Jörg-Rüdiger Sack, Arvind Gupta, and Roberto Tamassia, editors, Algorithms and Data Structures: 6th International Workshop, WADS'99 Vancouver, Canada, August 11-14, 1999 Proceedings, pages 205-216, Berlin, Heidelberg, 1999. Springer Berlin Heidelberg. URL:
  6. Jyrki Katajainen. Worst-case-efficient dynamic arrays in practice. In Andrew V. Goldberg and Alexander S. Kulikov, editors, Experimental Algorithms: 15th International Symposium, SEA 2016, St. Petersburg, Russia, June 5-8, 2016, Proceedings, pages 167-183, Cham, 2016. Springer International Publishing. URL:
  7. Jyrki Katajainen and Bjarke Buur Mortensen. Experiences with the design and implementation of space-efficient deques. In Gerth Stølting Brodal, Daniele Frigioni, and Alberto Marchetti-Spaccamela, editors, Algorithm Engineering: 5th International Workshop, WAE 2001 Århus, Denmark, August 28-31, 2001 Proceedings, pages 39-50, Berlin, Heidelberg, 2001. Springer Berlin Heidelberg. URL:
  8. Rajeev Raman, Venkatesh Raman, and S. Srinivasa Rao. Succinct dynamic data structures. In Frank Dehne, Jörg-Rüdiger Sack, and Roberto Tamassia, editors, Algorithms and Data Structures: 7th International Workshop, WADS 2001 Providence, RI, USA, August 8-10, 2001 Proceedings, pages 426-437, Berlin, Heidelberg, 2001. Springer Berlin Heidelberg. URL:
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail