research-article

Thin heaps, thick heaps

Authors:

Robert Endre TarjanAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 4, Issue 1

Article No.: 3, Pages 1 - 14

https://doi.org/10.1145/1328911.1328914

Published: 28 March 2008 Publication History

Abstract

The Fibonacci heap was devised to provide an especially efficient implementation of Dijkstra's shortest path algorithm. Although asyptotically efficient, it is not as fast in practice as other heap implementations. Expanding on ideas of Høyer [1995], we describe three heap implementations (two versions of thin heaps and one of thick heaps) that have the same amortized efficiency as Fibonacci heaps, but need less space and promise better practical performance. As part of our development, we fill in a gap in Høyer's analysis.

References

[1]

Adel'son-Vel'skii, G. M., and Landis, E. M. 1962. An algorithm for organization of information. Dokl. Akad. Nauk SSSR 146, 263--266.

[2]

Aho, A. V., Hopcroft, J. E., and Ullman, J. D. 1982. Data Structures and Algorithms. Addison-Wesley.

Digital Library

[3]

Arge, L., Bender, M. A., Demaine, E. D., Holland-Minkley, B., and Munro, J. I. 2002. Cache-Oblivious priority queue and graph algorithm applications. In Proceedings of the 34th ACM Symposium on Theory of Computing (STOC). ACM Press, 268--276.

Digital Library

[4]

Bayer, R. 1972. Symmetric binary b-trees: Data structure and maintenance algorithms. Acta Inf. 1, 290--306.

Digital Library

[5]

Ben-Amram, A. M. 1995. What is a “pointer machine”&quest; SIGACT News 26, 2, 88--95.

Digital Library

[6]

Brodal, G. S. 1996. Worst-Case priority queues. In Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). ACM Press, 52--58.

Digital Library

[7]

Brodal, G. S. 1995. Fast meldable priority queues. In Proceedings of the 4th International Workshop on Algorithms and Data Structures (WADS). Lecture Notes in Computer Science, vol. 955. Springer, 282--290.

Digital Library

[8]

Brodal, G. S., and Fagerberg, R. 2002. Funnel heap---A cache oblivious priority queue. In Proceedings of the 13th Annual International Symposium on Algorithms and Computation (ICALP). Lecture Notes in Computer Science, vol. 2518. Springer, 219--228.

Digital Library

[9]

Brodal, G. S., Fagerberg, R., Meyer, U., and Zeh, N. 2004. Cache-Oblivious data structures and algorithms for undirected breadth-first search and shortest paths. In Proceedings of the 9th Scandinavian Workshop on Algorithm Theory (SWAT). Lecture Notes in Computer Science, vol. 3111. Springer, 480--492.

[10]

Brown, M. R. 1978. Implementation and analysis of binomial queue algorithms. SIAM J. Comput. 7, 3, 298--319.

Digital Library

[11]

Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C. 2001. Introduction to Algorithms, 2nd ed. MIT Press, Cambridge, MA.

Digital Library

[12]

Driscoll, J. R., Gabow, H. N., Shrairman, R., and Tarjan, R. E. 1988. Relaxed heaps: An alternative to Fibonacci heaps with applications to parallel computation. Commun. ACM 31, 11, 1343--1354.

Digital Library

[13]

Elmasry, A. 2004a. Layered heaps. In Proceedings of the 9th Scandinavian Workshop on Algorithm Theory (SWAT). Lecture Notes in Computer Science, vol. 3111. Springer.

[14]

Elmasry, A. 2004b. Parameterized self-adjusting heaps. J. Algor. 52, 2, 103--119.

Digital Library

[15]

Fredman, M. L. 1999a. On the efficiency of pairing heaps and related data structures. J. ACM 46, 4, 473--501.

Digital Library

[16]

Fredman, M. L. 1999b. A priority queue transform. In Proceedings of the 3rd International Workshop on Algorithm Engineering (WAE). Lecture Notes in Computer Science, vol. 1668. Springer, 243--257.

Digital Library

[17]

Fredman, M. L., and Willard, D. E. 1994. Trans-Dichotomous algorithms for minimum spanning trees and shortest paths. J. Comput. Syst. Sci. 48, 3, 533--551.

Digital Library

[18]

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

Digital Library

[19]

Fredman, M. L., Sedgewick, R., Sleator, D. D., and Tarjan, R. E. 1986. The pairing heap: A new form of self-adjusting heap. Algorithmica 1, 111--129.

Digital Library

[20]

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

Digital Library

[21]

Guibas, L. J., and Sedgewick, R. 1978. A dichromatic framework for balanced trees. In Proceedings of the Annual Symposium on Foundations of Computer Science (FOCS), 8--21.

[22]

Høyer, P. 1995. A general technique for implementation of efficient priority queues. In Proceedings of the 3rd Israel Symposium on Theory of Computer Systems. IEEE Computer Society Press, 57--66.

Digital Library

[23]

Kaplan, H., and Tarjan, R. E. 1999. New heap data structures. Tech. Rep. TR-597-99, Princeton University.

[24]

Kaplan, H., Shafrir, N., and Tarjan, R. E. 2002. Meldable heaps and Boolean union-find. In Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC), 573--582.

Digital Library

[25]

Knuth, D. E. 1997. The Art of Computer Programming, Volume 1: Fundamental Algorithms, 3rd ed. Addison-Wesley, Reading, MA.

Digital Library

[26]

Peterson, G. L. 1987. A balanced tree scheme for meldable heaps with updates. Tech. Rep. GIT-ICS-87-23, School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia.

[27]

Pettie, S. 2005. Towards a final analysis of pairing heaps. In Proceedings of the 46th Annual Symposium on Foundations of Computer Science (FOCS). 174--183.

Digital Library

[28]

Sleator, D., and Tarjan, R. E. 1986. Self-Adjusting heaps. SIAM J. Comput. 15, 1, 52--69.

Digital Library

[29]

Stasko, J. T., and Vitter, J. S. 1987. Pairing heaps: Experiments and analysis. Commun. ACM 30, 3, 234--249.

Digital Library

[30]

Takaoka, T. 2003. Theory of 2-3 heaps. Discrete Appl. Math. 126, 1, 115--128.

Digital Library

[31]

Takaoka, T. 2000. Theory of trinomial heaps. In Proceedings of the 6th Annual International Conference on Computing and Combinatorics (COCOON). Lecture Notes in Computer Science, vol. 1858. Springer, 362--372.

Digital Library

[32]

Tarjan, R. E. 1979. A class of algorithms which require nonlinear time to maintain disjoint sets. J. Comput. Syst. Sci. 18, 2, 110--127.

[33]

Tarjan, R. E. 1985. Amortized computational complexity. SIAM J. Algebr. Discrete Meth. 6, 2, 306--318.

[34]

Tarjan, R. E. 1982. Data Structures and Network Algorithms. SIAM, Philadelphia, PA.

Digital Library

[35]

Thorup, M. 2004. Integer priority queues with decrease key in constant time and the single source shortest paths problem. J. Comput. Syst. Sci. 69, 3, 330--353.

Digital Library

[36]

Vuillemin, J. 1978. A data structure for manipulating priority queues. Commun. ACM 21, 309--314.

Digital Library

Cited By

Brodal GLagogiannis GTarjan R(2024)Strict Fibonacci HeapsACM Transactions on Algorithms10.1145/370769221:2(1-18)Online publication date: 10-Dec-2024
https://dl.acm.org/doi/10.1145/3707692
Kozma LSaranurak T(2019)Smooth Heaps and a Dual View of Self-Adjusting Data StructuresSIAM Journal on Computing10.1137/18M1195188(STOC18-45-STOC18-93)Online publication date: 5-Nov-2019
https://doi.org/10.1137/18M1195188
Kozma LSaranurak TDiakonikolas IKempe DHenzinger M(2018)Smooth heaps and a dual view of self-adjusting data structuresProceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3188745.3188864(801-814)Online publication date: 20-Jun-2018
https://dl.acm.org/doi/10.1145/3188745.3188864
Show More Cited By

Index Terms

Thin heaps, thick heaps
1. Information systems
  1. Information storage systems
    1. Record storage systems
      1. Record storage alternatives
2. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 4, Issue 1

March 2008

343 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1328911

Issue’s Table of Contents

Copyright © 2008 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 March 2008

Accepted: 01 September 2007

Revised: 01 September 2006

Received: 01 April 2005

Published in TALG Volume 4, Issue 1

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Cited By

Brodal GLagogiannis GTarjan R(2024)Strict Fibonacci HeapsACM Transactions on Algorithms10.1145/370769221:2(1-18)Online publication date: 10-Dec-2024
https://dl.acm.org/doi/10.1145/3707692
Kozma LSaranurak T(2019)Smooth Heaps and a Dual View of Self-Adjusting Data StructuresSIAM Journal on Computing10.1137/18M1195188(STOC18-45-STOC18-93)Online publication date: 5-Nov-2019
https://doi.org/10.1137/18M1195188
Kozma LSaranurak TDiakonikolas IKempe DHenzinger M(2018)Smooth heaps and a dual view of self-adjusting data structuresProceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3188745.3188864(801-814)Online publication date: 20-Jun-2018
https://dl.acm.org/doi/10.1145/3188745.3188864
Hansen TKaplan HTarjan RZwick U(2017)Hollow HeapsACM Transactions on Algorithms10.1145/309324013:3(1-27)Online publication date: 27-Jul-2017
https://dl.acm.org/doi/10.1145/3093240
Li JPeebles J(2015)Replacing Mark Bits with Randomness in Fibonacci HeapsAutomata, Languages, and Programming10.1007/978-3-662-47672-7_72(886-897)Online publication date: 20-Jun-2015
https://doi.org/10.1007/978-3-662-47672-7_72
Hansen TKaplan HTarjan RZwick U(2015)Hollow HeapsAutomata, Languages, and Programming10.1007/978-3-662-47672-7_56(689-700)Online publication date: 20-Jun-2015
https://doi.org/10.1007/978-3-662-47672-7_56
Larkin DSen STarjan R(2014)A back-to-basics empirical study of priority queuesProceedings of the Meeting on Algorithm Engineering & Expermiments10.5555/2790174.2790181(61-72)Online publication date: 5-Jan-2014
https://dl.acm.org/doi/10.5555/2790174.2790181
Kaplan HTarjan RZwick U(2013)Soft Heaps SimplifiedSIAM Journal on Computing10.1137/12088018542:4(1660-1673)Online publication date: Jan-2013
https://doi.org/10.1137/120880185
Chan T(2013)Quake Heaps: A Simple Alternative to Fibonacci HeapsSpace-Efficient Data Structures, Streams, and Algorithms10.1007/978-3-642-40273-9_3(27-32)Online publication date: 2013
https://doi.org/10.1007/978-3-642-40273-9_3
Brodal G(2013)A Survey on Priority QueuesSpace-Efficient Data Structures, Streams, and Algorithms10.1007/978-3-642-40273-9_11(150-163)Online publication date: 2013
https://doi.org/10.1007/978-3-642-40273-9_11
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