Skip to main content
SpringerLink
Log in
Book cover

Workshop on Algorithms and Data Structures

WADS 2005: Algorithms and Data Structures pp 49–60Cite as

The Complexity of Implicit and Space Efficient Priority Queues

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3608))

Abstract

In this paper we study the time-space complexity of implicit priority queues supporting the decreasekey operation. Our first result is that by using one extra word of storage it is possible to match the performance of Fibonacci heaps: constant amortized time for insert and decreasekey and logarithmic time for deletemin. Our second result is a lower bound showing that that one extra word really is necessary. We reduce the decreasekey operation to a cell-probe type game called the Usher’s Problem, where one must maintain a simple data structure without the aid of any auxiliary storage.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andersson, A., Hagerup, T., Hastad, J., Petersson, O.: Tight bounds for searching a sorted array of strings. SIAM J. Comput. 30(5), 1552–1578 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Blum, M., Floyd, R.W., Pratt, V., Rivest, R.L., Tarjan, R.E.: Time bounds for selection. J. Comput. Syst. Sci. 7(4), 448–461 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  3. Brodnik, A., Carlsson, S., Demaine, E., Munro, J.I., Sedgewick, R.: Resizable arrays in optimal time and space. In: WADS, p. 37 (1999)

    Google Scholar 

  4. Brodnik, A., Munro, J.I.: Membership in constant time and almost-minimum space. SIAM J. Comput. 28(5), 1627–1640 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Carlsson, S., Munro, J.I., Poblete, P.V.: An implicit binomial queue with constant insertion time. In: SWAT, pp. 1–13 (1988)

    Google Scholar 

  6. Driscoll, J.R., Gabow, H.N., Shrairman, R., Tarjan, R.E.: Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation. Comm. ACM 31(11), 1343–1354 (1988)

    Article  MathSciNet  Google Scholar 

  7. Fiat, A., Naor, M.: Implicit O(1) probe search. SIAM J. Comput. 22(1), 1–10 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Fiat, A., Naor, M., Schmidt, J.P., Siegel, A.: Nonoblivious hashing. J. ACM 39(4), 764–782 (1992)

    MATH  MathSciNet  Google Scholar 

  9. Franceschini, G., Grossi, R.: Optimal worst-case operations for implicit cache-oblivious search trees. In: Proc. 8th WADS (2003)

    Google Scholar 

  10. Franceschini, G., Grossi, R.: No sorting? better searching! In: Proc. 45th IEEE Symp. on Foundations of Computer Science (FOCS), pp. 491–498 (2004)

    Google Scholar 

  11. Fredman, M.L.: On the efficiency of pairing heaps and related data structures. J. ACM 46(4), 473–501 (1999)

    MATH  MathSciNet  Google Scholar 

  12. Fredman, M.L., Sedgewick, R., Sleator, D.D., Tarjan, R.E.: The pairing heap: a new form of self-adjusting heap. Algorithmica 1(1), 111–129 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  13. Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34(3), 596–615 (1987)

    MathSciNet  Google Scholar 

  14. Hagerup, T., Raman, R.: An efficient quasidictionary. In: Penttonen, M., Schmidt, E.M. (eds.) SWAT 2002. LNCS, vol. 2368, p. 1. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  15. Harvey, N.J.A., Zatloukal, K.: The post-order heap. In: Proc. FUN (2004)

    Google Scholar 

  16. Iacono, J.: Improved upper bounds for pairing heaps. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 32–43. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  17. Johnson, D.B.: Priority queues with update and finding minimum spanning trees. Info. Proc. Lett. 4(3), 53–57 (1975)

    Article  MATH  Google Scholar 

  18. Kaplan, H., Tarjan, R.E.: New heap data structures. Technical Report TR-597-99, Computer Science Dept., Princeton University (March 1999)

    Google Scholar 

  19. Mortensen, C.W., Pettie, S.: The complexity of implicit and space-efficient priority queues. Manuscript (2005), http://www.mpi-sb.mpg.de/~pettie/

  20. Munro, J.I.: An implicit data structure supporting insertion, deletion, and search in \(O({\rm log}\sp 2\, n)\) time. J. Comput. Syst. Sci. 33(1), 66–74 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  21. Munro, J.I., Suwanda, H.: Implicit data structures for fast search and update. J. Comput. Syst. Sci. 21(2), 236–250 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  22. Pagh, R.: Low redundancy in static dictionaries with constant query time. SIAM J. Comput. 31(2), 353–363 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  23. Raman, R., Raman, V., Rao, S.S.: Succinct indexable dictionaries with applications to encoding k-ary trees and multisets. In: SODA, pp. 233–242 (2002)

    Google Scholar 

  24. Raman, R., Rao, S.S.: Succinct dynamic dictionaries and trees. In: Proc. 30th Int’l Colloq. on Automata, Languages and Programming (2003)

    Google Scholar 

  25. Takaoka, T.: Theory of 2–3 heaps. Discrete Appl. Math. 126(1), 115–128 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  26. Williams, J.W.J.: Algorithm 232 (heapsort). Comm. ACM 7, 347–348 (1964)

    Google Scholar 

  27. Yao, A.C.C.: Should tables be sorted? J. ACM 28(3), 615–628 (1981)

    MATH  Google Scholar 

  28. Zuckerman, D.: Computing Efficiently Using General Weak Random Sources. Ph.D. Thesis, The University of California at Berkeley (August 1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IT University of Copenhagen,  

    Christian W. Mortensen

  2. Max Planck Institut für Informatik,  

    Seth Pettie

Authors
  1. Christian W. Mortensen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seth Pettie
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Cheriton School of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ont., Canada

    Alejandro López-Ortiz

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada

    Jörg-Rüdiger Sack

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mortensen, C.W., Pettie, S. (2005). The Complexity of Implicit and Space Efficient Priority Queues. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_6

Download citation

  • DOI: https://doi.org/10.1007/11534273_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28101-6

  • Online ISBN: 978-3-540-31711-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation