Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Approximate Dictionaries

  • Venkatesh Srinivasan
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_16

Years and Authors of Summarized Original Work

  • 2002; Buhrman, Miltersen, Radhakrishnan, Venkatesh

Problem Definition

The Problem and the Model

A static data structure problem consists of a set of data D, a set of queries Q, a set of answers A, and a function \(f : D \times Q \rightarrow A\)

Keywords

Cell probe model Data structures Static membership 
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Recommended Reading

  1. 1.
    Alon N and Feige U (2009) On the power of two, three and four probes. In: Proceedings of SODA’09, New York, pp 346–354Google Scholar
  2. 2.
    Brodnik A, Munro JI (1994) Membership in constant time and minimum space. In: Algorithms ESA’94: second annual European symposium, Utrecht. Lecture notes in computer science, vol 855, pp 72–81. Final version: Membership in constant time and almost-minimum space. SIAM J Comput 28(5):1627–1640 (1999)Google Scholar
  3. 3.
    Buhrman H, Miltersen PB, Radhakrishnan J, Venkatesh S (2002) Are bitvectors optimal? SIAM J Comput 31(6):1723–1744MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Chen V, Grigorescu E, de Wolf R (2013) Error-correcting data structures. SIAM J Comput 42(1):84–111MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Dyachkov AG, Rykov VV (1982) Bounds on the length of disjunctive codes. Problemy Peredachi Informatsii 18(3):7–13 [Russian]MathSciNetzbMATHGoogle Scholar
  6. 6.
    Elias P, Flower RA (1975) The complexity of some simple retrieval problems. J Assoc Comput Mach 22:367–379MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Erdős P, Frankl P, Füredi Z (1985) Families of finite sets in which no set is covered by the union of r others. Isr J Math 51:79–89MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Fiat A, Naor M (1993) Implicit O(1) probe search. SIAM J Comput 22:1–10MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Fiat A, Naor M, Schmidt JP, Siegel A (1992) Non-oblivious hashing. J Assoc Comput Mach 31:764–782MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Fredman ML, Komlós J, Szemerédi E (1984) Storing a sparse table with O(1) worst case access time. J Assoc Comput Mach 31(3):538–544MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Füredi Z (1996) On r-cover-free families. J Comb Theory Ser A 73:172–173MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Garg M, Radhakrishnan J (2015) Set membership with a few bit probes. In: Proceedings of SODA’15, San Diego, pp 776–784Google Scholar
  13. 13.
    Katz J, Trevisan L (2000) On the efficiency of local decoding procedures for error-correcting codes. In: Proceedings of STOC’00, Portland, pp 80–86Google Scholar
  14. 14.
    Lewenstein M, Munro JI, Nicholson PK, Raman V (2014) Improved explicit data structures in the bitprobe model. In: Proceedings of ESA’14, Wroclaw, pp 630–641Google Scholar
  15. 15.
    Miltersen PB, Nisan N, Safra S, Wigderson A (1998) On data structures and asymmetric communication complexity. J Comput Syst Sci 57:37–49MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Minsky M, Papert S (1969) Perceptrons. MIT, CambridgezbMATHGoogle Scholar
  17. 17.
    Pagh R (1999) Low redundancy in static dictionaries with O(1) lookup time. In: Proceedings of ICALP ’99, Prague. Lecture notes in computer science, vol 1644, pp 595–604Google Scholar
  18. 18.
    Radhakrishnan J, Raman V, Rao SS (2001) Explicit deterministic constructions for membership in the bitprobe model. In: Proceedings of ESA’01, Aarhus, pp 290–299Google Scholar
  19. 19.
    Radhakrishnan J, Shah S, Shannigrahi S (2010) Data structures for storing small sets in the bitprobe model. In: Proceedings of ESA’10, Liverpool, pp 159–170Google Scholar
  20. 20.
    Ruszinkó M (1984) On the upper bound of the size of r-cover-free families. J Comb Theory Ser A 66:302–310MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Ta-Shma A (2002) Explicit one-probe storing schemes using universal extractors. Inf Process Lett 83(5):267–274MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Viola E (2012) Bit-probe lower bounds for succinct data structures. SIAM J Comput 41(6):1593–1604MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Yao ACC (1981) Should tables be sorted? J Assoc Comput Mach 28(3):615–628MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Computer Science, University of VictoriaVictoriaCanada