Monotone minimal perfect hashing: Searching a sorted table with O(1) accesses

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2009, Pages 785-794

  Belazzougui, Djamal ^a   Boldi, Paolo ^b   Pagh, Rasmus ^c   Vigna, Sebastiano ^b  

^a Institut National de Formation en Informatique   (Algeria)

^b UNIVERSITY OF MILAN   (Italy)

^c IT UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

QUERY PROCESSING;

A-MONOTONE; BIJECTIONS; CONSTANT TIME; FUNCTION MAPS; LOWER BOUNDS; MINIMAL PERFECT HASHES; MINIMAL PERFECT HASHING; QUERY TIME;

HASH FUNCTIONS;

EID: 70349105927     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973068.86     Document Type: Conference Paper

References (27)

1. M. A. Bender, Z. Duan, J. Iacono, and J. Wu. A locality-preserving cache-oblivious dynamic dictionary. J. Algorithms, 53(2):115-136, 2004.
2. G. S. Brodal, R. Fagerberg, and R. Jacob. Cache oblivious search trees via binary trees of small height. In Proceedings of the 13th Annual ACM-SIAM Symposium On Discrete Mathematics (SODA-02), pages 39-48, New York, Jan. 6-8 2002. ACM Press.
3. J. L. Carter and M. N. Wegman. Universal classes of hash functions. J. Comput. Syst. Sci., 18:143-154, 1979.
4. L. Carter, R. Floyd, J. Gill, G. Markowsky, and M. Wegman. Exact and approximate membership testers. In Proceedings of Symposium on Theory of Computation (STOC '78), pages 59-65. ACM Press, 1978.
5. D. Charles and K. Chellapilla. Bloomier filters: A second look. In Proc. ESA 2008, 2008.
6. D. R. Clark and J. I. Munro. Efficient suffix trees on secondary storage (extended abstract). In SODA, pages 383-391, 1996.
7. M. Dietzfelbinger, J. Gil, Y. Matias, and N. Pippenger. Polynomial hash functions are reliable (extended abstract). In 19th International Colloquium on Automata, Languages and Programming (ICALP '92), volume 623 of Lecture Notes in Computer Science, pages 235-246. Springer, 1992.
8. M. Dietzfelbinger and R. Pagh. Succinct data structures for retrieval and approximate membership (extended abstract). In L. Aceto, I. Damgård, L. A. Goldberg, M. M. Halldórsson, A. Ingólfsdóttir, and I. Walukiewicz, editors, Automata, Languages and Programming, 35th International Colloquium, ICALP 2008, Reykjavik, Iceland, July 7-11, 2008, Proceedings, Part I: Tack A: Algorithms, Automata, Complexity, and Games, volume 5125 of Lecture Notes in Computer Science, pages 385-396. Springer, 2008.
9. A. Fiat and M. Naor. Implicit O(1) probe search. SIAM Journal of Computing, 22(1):1-10, 1993.
10. A. Fiat, M. Naor, J. P. Schmidt, and A. Siegel. Nonoblivious hashing. Journal of the ACM, 39(4):764-782, 1992.
11. E. A. Fox, Q. F. Chen, A. M. Daoud, and L. S. Heath. Order-preserving minimal perfect hash functions and information retrieval. ACM Trans. Inf. Sys., 9(3):281-308, 1991.
12. M. L. Fredman and J. Komlós. On the size of separating systems and families of perfect hash functions. SIAM J. Algebraic Discrete Methods, 5(1):61-68, 1984.
13. M. L. Fredman, J. Komlós, and E. Szemerédi. Storing a sparse table with O(1) worst case access time. J. Assoc. Comput. Mach., 31(3):538-544, July 1984.
14. A. Gupta, W.-K. Hon, R. Shah, and J. S. Vitter. Compressed data structures: Dictionaries and data-aware measures. Theoret. Comput. Sci., 387(3):313-331, 2007.
15. T. Hagerup and T. 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, 2001.
16. G. Jacobson. Space-efficient static trees and graphs. In In Proc 30th Annual Symposium on Foundations of Computer Science, pages 549-554, 1989.
17. D. E. Knuth. Sorting and Searching, volume 3 of The Art of Computer Programming. Addison-Wesley, second edition, 1997.
18. H. G. Mairson. The program complexity of searching a table. In 24th Annual Symposium on Foundations of Computer Science, pages 40-47, Tucson, Arizona, 7-9 Nov. 1983. IEEE.
19. H. G. Mairson. The effect of table expansion on the program complexity of perfect hash functions. BIT, 32(3):430-440, Sept. 1992.
20. B. S. Majewski, N. C. Wormald, G. Havas, and Z. J. Czech. A family of perfect hashing methods. Comput. J., 39(6):547-554, 1996.
21. K. Mehlhorn. On the program size of perfect and universal hash functions. In 23th Annual Symposium on Foundations of Computer Science (FOCS 1982), pages 170-175, Chicago, Illinois, USA, 1982. IEEE.
22. R. Pagh. Low redundancy in static dictionaries with constant query time. SIAM J. Comput., 31(2):353-363, 2001.
23. E. Porat. An optimal bloom filter replacement based on matrix solving, 2008. arXiv:0804.1845v1.
24. V. Raman. Locality preserving dictionaries: theory & application to clustering in databases. In PODS '99: Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, pages 337-345, New York, NY, USA, 1999. ACM.
25. J. P. Schmidt and A. Siegel. The spatial complexity of oblivious k-probe hash functions. SIAM Journal of Computing, 19(5):775-786, 1990.
26. D. E. Willard. Log-logarithmic worst-case range queries are possible in space theta(n). Inf. Process. Lett., 17(2):81-84, 1983.
27. A. C.-C. Yao. Should tables be sorted? J. Assoc. Comput. Mach., 28(3):615-628, 1981.