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Policy-Based Benchmarking of Weak Heaps and Their Relatives,

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Experimental Algorithms (SEA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6049))

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Abstract

In this paper we describe an experimental study where we evaluated the practical efficiency of three worst-case efficient priority queues: 1) a weak heap that is a binary tree fulfilling half-heap ordering, 2) a weak queue that is a forest of perfect weak heaps, and 3) a run-relaxed weak queue that extends a weak queue by allowing some nodes to violate half-heap ordering. All these structures support Delete and Delete-min in logarithmic worst-case time. A weak heap supports Insert and Decrease in logarithmic worst-case time, whereas a weak queue reduces the worst-case running time of Insert to O(1), and a run-relaxed weak queue that of both Insert and Decrease to O(1). As competitors to these structures, we considered a binary heap, a Fibonacci heap, and a pairing heap. Generic programming techniques were heavily used in the code development. For benchmarking purposes we developed several component frameworks that could be instantiated with different policies.

Research partially supported by DFG grant ED 74/8-1.

Partially supported by the Danish Natural Science Research Council under contract 09-060411 (project “Generic programming—algorithms and tools”).

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References

  1. Aho, A.V., Lam, M.S., Sethi, R., Ullman, J.D.: Compilers: Principles, Techniques, & Tools, 2nd edn. Pearson Education, Inc., London (2007)

    Google Scholar 

  2. Alexandrescu, A.: Modern C++ Design: Generic Programming and Design Patterns Applied. Addison-Wesley, Reading (2001)

    Google Scholar 

  3. 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 

  4. Brown, M.R.: Implementation and analysis of binomial queue algorithms. SIAM Journal on Computing 7(3), 298–319 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bruun, A.: Effektivitetsmåling på krydsninger af svage og binomiale prioritetskøer, CPH STL Report 2010-2, Department of Computer Science, University of Copenhagen (2010)

    Google Scholar 

  6. Chan, T.M.: Quake heaps: A simple alternative to Fibonacci heaps (2009) (unpublished manuscript)

    Google Scholar 

  7. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, Cambridge (2009)

    MATH  Google Scholar 

  8. Department of Computer Science, University of Copenhagen, The CPH STL (2000–2010), Website accessible at http://cphstl.dk/

  9. 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)

    Article  MathSciNet  Google Scholar 

  10. Dutton, R.D.: Weak-heap sort. BIT 33(3), 372–381 (1993)

    Article  MathSciNet  Google Scholar 

  11. Edelkamp, S.: Rank-relaxed weak queues: Faster than pairing and Fibonacci heaps? Technical Report 54, TZI, Universität Bremen (2009)

    Google Scholar 

  12. Edelkamp, S., Wegener, I.: On the performance of Weak-Heapsort. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 254–266. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  13. Elmasry, A.: Violation heaps: A better substitute for Fibonacci heaps, E-print 0812.2851v1, arXiv.org (2008)

    Google Scholar 

  14. 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 

  15. 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 

  16. 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)

    Article  MathSciNet  Google Scholar 

  17. Haeupler, B., Sen, S., Tarjan, R.E.: Rank-pairing heaps. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 659–670. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  18. Jensen, C.: Private communication (2009)

    Google Scholar 

  19. Katajainen, J.: Project proposal: A meldable, iterator-valid priority queue, CPH STL Report 2005-1, Department of Computer Science, University of Copenhagen (2005)

    Google Scholar 

  20. Katajainen, J.: Priority-queue frameworks: Programs, CPH STL Report 2009-7, Department of Computer Science, University of Copenhagen (2009)

    Google Scholar 

  21. Katajainen, J., Mortensen, B.B.: Experiences with the design and implementation of space-efficient deques. In: Brodal, G.S., Frigioni, D., Marchetti-Spaccamela, A. (eds.) WAE 2001. LNCS, vol. 2141, pp. 39–50. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  22. Knuth, D.E.: Fundamental Algorithms, 3rd edn. The Art of Computer Programming, vol. 1. Addison Wesley Longman, Amsterdam (1997)

    MATH  Google Scholar 

  23. Knuth, D.E.: Sorting and Searching, 2nd edn. The Art of Computer Programming, vol. 3. Addison-Wesley Longman, Amsterdam (1998)

    Google Scholar 

  24. Mehlhorn, K., Näher, S.: The LEDA Platform of Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  25. Mehlhorn, K., Sanders, P.: Algorithms and Data Structures: The Basic Toolbox. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  26. Paredes, R.: Graphs for metric space searching, Ph.D. Thesis, Department of Computer Science, University of Chile (2008)

    Google Scholar 

  27. Rasmussen, J.: Implementing run-relaxed weak queues, CPH STL Report 2008-1, Department of Computer Science, University of Copenhagen (2008)

    Google Scholar 

  28. Stasko, J.T., Vitter, J.S.: Pairing heaps: Experiments and analysis. Communications of the ACM 30(3), 234–249 (1987)

    Article  MathSciNet  Google Scholar 

  29. Vuillemin, J.: A data structure for manipulating priority queues. Communications of the ACM 21(4), 309–315 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  30. Wegener, I.: Bottom-up-Heapsort, a new variant of Heapsort beating, on an average, Quicksort (if n is not very small). Theoretical Computer Science 118, 81–98 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  31. Williams, J.W.J.: Algorithm 232: Heapsort. Communications of the ACM 7(6), 347–348 (1964)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Copenhagen, Universitetsparken 1, 2100, Copenhagen East, Denmark

    Asger Bruun, Jyrki Katajainen & Jens Rasmussen

  2. TZI, Universität Bremen, Am Fallturm 1, 28357, Bremen, Germany

    Stefan Edelkamp

Authors
  1. Asger Bruun
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  2. Stefan Edelkamp
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  3. Jyrki Katajainen
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  4. Jens Rasmussen
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Applications, University of Napoli Federico II, Compl. MSA, Via Cintia, 80126, Napoli, Italy

    Paola Festa

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Bruun, A., Edelkamp, S., Katajainen, J., Rasmussen, J. (2010). Policy-Based Benchmarking of Weak Heaps and Their Relatives,. In: Festa, P. (eds) Experimental Algorithms. SEA 2010. Lecture Notes in Computer Science, vol 6049. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13193-6_36

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  • DOI: https://doi.org/10.1007/978-3-642-13193-6_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13192-9

  • Online ISBN: 978-3-642-13193-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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