Skip to main content
SpringerLink
Log in

Rank-Pairing Heaps

  • Conference paper
Algorithms - ESA 2009 (ESA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5757))

Included in the following conference series:

Abstract

We introduce the rank-pairing heap, a heap (priority queue) implementation that combines the asymptotic efficiency of Fibonacci heaps with much of the simplicity of pairing heaps. Unlike all other heap implementations that match the bounds of Fibonacci heaps, our structure needs only one cut and no other structural changes per key decrease; the trees representing the heap can evolve to have arbitrary structure. Our initial experiments indicate that rank-pairing heaps perform almost as well as pairing heaps on typical input sequences and better on worst-case sequences.

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

Access this chapter

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brodal, G.: Worst-case efficient priority queues. In: SODA, pp. 52–58 (1996)

    Google Scholar 

  2. Brown, M.R.: Implementation and analysis of binomial queue algorithms. SIAM J. Comput., 298–319 (1978)

    Google Scholar 

  3. Chan, T.M.: Quake heaps: a simple alternative to Fibonacci heaps (2009)

    Google Scholar 

  4. Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  5. 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 

  6. Edmonds, J.: Optimum branchings. J. Res. Nat. Bur. Standards B71, 233–240 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  7. Elmasry, A.: Violation heaps: A better substitute for Fibonacci heaps. CoRR (2008)

    Google Scholar 

  8. Elmasry, A.: Pairing heaps with O(loglogn) decrease cost. In: SODA, pp. 471–476 (2009)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. 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  MathSciNet  MATH  Google Scholar 

  11. Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. In: FOCS, pp. 338–346, 24–26 (1984)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  13. Gabow, H.N., Galil, Z., Spencer, T.H., Tarjan, R.E.: Efficient algorithms for finding minimum spanning trees in undirected and directed graphs. Combinatorica 6(2), 109–122 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  14. Høyer, P.: A general technique for implementation of efficient priority queues. In: ISTCS, pp. 57–66 (1995)

    Google Scholar 

  15. Kaplan, H., Shafrir, N., Tarjan, R.E.: Meldable heaps and boolean union-find. In: STOC, pp. 573–582 (2002)

    Google Scholar 

  16. Kaplan, H., Tarjan, R.E.: New heap data structures. Technical Report TR-597-99, Princeton Univ. (1999)

    Google Scholar 

  17. Kaplan, H., Tarjan, R.E.: Thin heaps, thick heaps. ACM Trans. Alg. 4(1), 1–14 (2008)

    Article  MathSciNet  Google Scholar 

  18. Knuth, D.E.: The Art of Computer Programming. Fundamental Algorithms, vol. 1. Addison-Wesley, Reading (1973)

    MATH  Google Scholar 

  19. Knuth, D.E.: The Art of Computer Programming. Sorting and Searching, vol. 3. Addison-Wesley, Reading (1973)

    MATH  Google Scholar 

  20. Liao, A.M.: Three priority queue applications revisited. Algorithmica 7, 415–427 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  21. Moret, B., Shapiro, H.: An empirical analysis of algorithms for constructing a minimum spanning tree. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1991. LNCS, vol. 519, pp. 400–411. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  22. Nagamochi, H., Ibaraki, T.: Computing edge-connectivity in multigraphs and capacitated graphs. J. Disc. Math. 5(1), 54–66 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  23. Peterson, G.L.: A balanced tree scheme for meldable heaps with updates. Technical Report GIT-ICS-87-23, Georgia Inst. of Tech (1987)

    Google Scholar 

  24. Pettie, S.: Towards a final analysis of pairing heaps. In: FOCS, pp. 174–183 (2005)

    Google Scholar 

  25. Stasko, J.T., Vitter, J.S.: Pairing heaps: experiments and analysis. Comm. ACM 30(3), 234–249 (1987)

    Article  MathSciNet  Google Scholar 

  26. Tarjan, R.E.: Amortized computational complexity. J. Alg. Disc. Methods 6, 306–318 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  27. Various. The Fifth DIMACS Challenge—Priority Queue Tests (1996)

    Google Scholar 

  28. Vuillemin, J.: A data structure for manipulating priority queues. Comm. ACM 21(4), 309–315 (1978)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, USA

    Bernhard Haeupler

  2. Princeton University, USA

    Siddhartha Sen & Robert E. Tarjan

  3. HP Laboratories, Palo Alto, CA, 94304

    Robert E. Tarjan

Authors
  1. Bernhard Haeupler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Siddhartha Sen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert E. Tarjan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Amos Fiat

  2. Fakultät für Informatik, Universität Karlsruhe (TH), Am Fasanengarten 5, 76131, Karlsruhe, Germany

    Peter Sanders

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Haeupler, B., Sen, S., Tarjan, R.E. (2009). Rank-Pairing Heaps. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_59

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04128-0_59

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04127-3

  • Online ISBN: 978-3-642-04128-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation