Article

On the cell probe complexity of membership and perfect hashing

Author:

Rasmus PaghAuthors Info & Claims

STOC '01: Proceedings of the thirty-third annual ACM symposium on Theory of computing

Pages 425 - 432

https://doi.org/10.1145/380752.380836

Published: 06 July 2001 Publication History

Abstract

We study two fundamental static data structure problems, membership and perfect hashing, in Yao's cell probe model. The first space and bit probe optimal worst case upper bound is given for the membership problem. We also give a new efficient membership scheme where the query algorithm makes just one adaptive choice, and probes a total of three words. A lower bound shows that two word probes generally do not suffice. For minimal perfect hashing we show a tight bit probe lower bound, and give a simple scheme achieving this performance, making just one adaptive choice. Linear range perfect hashing is shown to be implementable with the same number of bit probes, of which just one is adaptive. In contrast, we establish that for sufficiently sparse sets, non-adaptive perfect hashing needs exponentially more bit probes. This is the first such separation of adaptivity and non-adaptivity.

References

[1]

Yossi Azar, Andrei Z. Broder, Anna R. Karlin, and Eli Upfal. Balanced allocations. SIAM J. Comput., 29(1):180-200 (electronic), 1999.]]

Digital Library

[2]

Andrej Brodnik and J. Ian Munro. Membership in constant time and almost-minimum space. SIAM J. Comput., 28(5):1627-1640 (electronic), 1999.]]

Digital Library

[3]

Harry Buhrman, Peter Bro Miltersen, Jaikumar Radhakrishnan, and S. Venkatesh. Are bitvectors optimal? In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (STOC '00), pages 449-458. ACM Press, New York, 2000.]]

Digital Library

[4]

J. Lawrence Carter and Mark N. Wegman. Universal classes of hash functions. J. Comput. System Sci., 18(2):143-154, 1979.]]

[5]

Arthur Czumaj and Volker Stemann. Randomized allocation processes. In Proceedings of the 38th Annual Symposium on Foundations of Computer Science (FOCS '97), pages 194-203, Los Alamitos, CA, 1997. IEEE Comput. Soc. Press.]]

Digital Library

[6]

Shimon Even, Alon Itai, and Adi Shamir. On the complexity of timetable and multicommodity ow problems. SIAM J. Comput., 5(4):691-703, 1976.]]

Digital Library

[7]

Michael L. Fredman, Janos Komlos, and Endre Szemeredi. Storing a sparse table with O(1) worst case access time. J. Assoc. Comput. Mach., 31(3):538-544, 1984.]]

Digital Library

[8]

Ofer Gabber and Zvi Galil. Explicit constructions of linear-sized superconcentrators. J. Comput. System Sci., 22(3):407-420, 1981.]]

[9]

Torben Hagerup and Torsten Tholey. Efficient minimal perfect hashing in nearly minimal space. In Proceedings of the 18th Symposium on Theoretical Aspects of Computer Science (STACS '01), volume 2010 of Lecture Notes in Computer Science, pages 317-326. Springer-Verlag, Berlin, 2001.]]

Digital Library

[10]

Philip Hall. On representatives of subsets. J. London Math. Soc., 10:26-30, 1935.]]

[11]

Richard M. Karp, Michael Luby, and Friedhelm Meyer auf der Heide. Efficient PRAM simulation on a distributed memory machine. Algorithmica, 16(4-5):517-542, 1996.]]

[12]

Kurt Mehlhorn. Data structures and algorithms. 1, Sorting and searching. Springer-Verlag, Berlin, 1984.]]

[13]

Marvin Minsky and Seymour Papert. Perceptrons: An Introduction to Computational Geometry. MIT Press, Cambridge, MA, 1969.]]

Digital Library

[14]

Rasmus Pagh. Low Redundancy in Static Dictionaries with O(1) Lookup Time. In Proceedings of the 26th International Colloquium on Automata, Languages and Programming (ICALP '99), volume 1644 of Lecture Notes in Computer Science, pages 595-604. Springer-Verlag, Berlin, 1999.]]

Digital Library

[15]

Rasmus Pagh. Hash and Displace: Efficient Evaluation of Minimal Perfect Hash Functions. In Proceedings of the 6th international Workshop on Algorithms and Data Structures (WADS '99), volume 1663 of Lecture Notes in Computer Science, pages 49-54. Springer-Verlag, Berlin, 1999.]]

Digital Library

[16]

Rasmus Pagh and Flemming Friche Rodler. Cuckoo hashing. Manuscript, 2001.]]

[17]

Jeanette P. Schmidt and Alan Siegel. The spatial complexity of oblivious k-probe hash functions. SIAM J. Comput., 19(5):775-786, 1990.]]

Digital Library

[18]

Jeanette P. Schmidt, Alan Siegel, and Aravind Srinivasan. Chernoff-Hoeffding bounds for applications with limited independence. In Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '93), pages 331-340, New York, 1993. ACM Press.]]

Digital Library

[19]

Alan Siegel. On universal classes of fast high performance hash functions, their time-space tradeoff, and their applications. In Proceedings of the 30th Annual Symposium on Foundations of Computer Science (FOCS '89), pages 20-25. IEEE Comput. Soc. Press, Los Alamitos, CA, 1989.]]

Digital Library

[20]

Andrew C.-C. Yao. Should tables be sorted? J. Assoc. Comput. Mach., 28(3):615-628, 1981.]]

Digital Library

[21]

Andrew C.-C. Yao. Uniform hashing is optimal. J. Assoc. Comput. Mach., 32(3):687-693, 1985.]]

Digital Library

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cover image ACM Conferences

STOC '01: Proceedings of the thirty-third annual ACM symposium on Theory of computing

July 2001

755 pages

ISBN:1581133499

DOI:10.1145/380752

Copyright © 2001 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 06 July 2001

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STOC '01 Paper Acceptance Rate 83 of 230 submissions, 36%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Tian HZhang JYang LTang YZha C(2023)Multi-party Privacy Set Intersection protocol with an Untrusted Cloud ServerFrontiers in Computing and Intelligent Systems10.54097/fcis.v2i3.52152:3(68-74)Online publication date: 13-Feb-2023
https://doi.org/10.54097/fcis.v2i3.5215
Dalal KDevroye LMalalla E(2023)Two-Way Linear Probing RevisitedAlgorithms10.3390/a1611050016:11(500)Online publication date: 28-Oct-2023
https://doi.org/10.3390/a16110500
Yu H(2022)Nearly Optimal Static Las Vegas Succinct DictionarySIAM Journal on Computing10.1137/20M136364951:3(STOC20-174-STOC20-249)Online publication date: 2-May-2022
https://doi.org/10.1137/20M1363649
Yu HMakarychev KMakarychev YTulsiani MKamath GChuzhoy J(2020)Nearly optimal static Las Vegas succinct dictionaryProceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3357713.3384274(1389-1401)Online publication date: 22-Jun-2020
https://dl.acm.org/doi/10.1145/3357713.3384274
Baskara Yudha AKimura KZhou HSolihin Y(2020)Scalable and Fast Lazy Persistency on GPUs2020 IEEE International Symposium on Workload Characterization (IISWC)10.1109/IISWC50251.2020.00032(252-263)Online publication date: Oct-2020
https://doi.org/10.1109/IISWC50251.2020.00032
Damaschke P(2018)Saving Probe Bits by Cube DominationGraph-Theoretic Concepts in Computer Science10.1007/978-3-030-00256-5_12(139-151)Online publication date: 2-Sep-2018
https://doi.org/10.1007/978-3-030-00256-5_12
Sun YHua YFeng DYang LZuo PCao SGuo Y(2017)A Collision-Mitigation Cuckoo Hashing Scheme for Large-Scale Storage SystemsIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2016.259476328:3(619-632)Online publication date: 1-Mar-2017
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Pagh R(2016)Cuckoo HashingEncyclopedia of Algorithms10.1007/978-1-4939-2864-4_97(478-481)Online publication date: 22-Apr-2016
https://doi.org/10.1007/978-1-4939-2864-4_97
Yu Hua Bin Xiao Xue Liu Dan Feng (2015)The Design and Implementations of Locality-Aware Approximate Queries in Hybrid Storage SystemsIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2014.236749726:11(3194-3207)Online publication date: 1-Nov-2015
https://dl.acm.org/doi/10.1109/TPDS.2014.2367497
Sun YHua YFeng DYang LZuo PCao S(2015)MinCounter: An efficient cuckoo hashing scheme for cloud storage systems2015 31st Symposium on Mass Storage Systems and Technologies (MSST)10.1109/MSST.2015.7208292(1-7)Online publication date: May-2015
https://doi.org/10.1109/MSST.2015.7208292
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