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A Survey of Data Structures in the Bitprobe Model

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Book cover Space-Efficient Data Structures, Streams, and Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8066))

Abstract

In this paper we survey data structures in the bitprobe model [31,15,50,30,11]. This model was introduced by Minsky and Papert in their book “Perceptrons” [31], studied later in the context of retrieval problems by Elias and Flower [15], and generalized by Yao [50] to the cell probe model. In the bitprobe model, we concern ourselves with the number of bit accesses or bit flips that occur during a computation. We wish to analyze the trade-off between the space occupied by a data structure, and the number of bits accesses that must be made to it in order to answer queries. Each bit access is referred to as a probe in this model. Furthermore, the amount of computation permitted by the query algorithm to determine which bits to probe is a secondary concern.

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References

  1. Alon, N., Feige, U.: On the power of two, three and four probes. In: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2009, pp. 346–354. Society for Industrial and Applied Mathematics, Philadelphia (2009)

    Chapter  Google Scholar 

  2. Alt, H., Mehlhorn, K., Munro, J.I.: Partial match retrieval in implicit data structures. Inf. Process. Lett. 19(2), 61–65 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bloom, B.H.: Space/time trade-offs in hash coding with allowable errors. Communications of the ACM 13(7), 422–426 (1970)

    Article  MATH  Google Scholar 

  4. Blue, R.: The Bit Probe Model for Membership Queries: Non-Adaptive Bit Queries. Master’s thesis, University of Maryland (2009)

    Google Scholar 

  5. Borodin, A., Fich, F.E., Meyer auf der Heide, F., Upfal, E., Wigderson, A.: A tradeoff between search and update time for the implicit dictionary problem. Theor. Comput. Sci. 58, 57–68 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bose, P., Carmi, P., Jansens, D., Maheshwari, A., Morin, P., Smid, M.: Improved methods for generating quasi-Gray codes. In: Kaplan, H. (ed.) SWAT 2010. LNCS, vol. 6139, pp. 224–235. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Brodal, G.S., Greve, M., Pandey, V., Rao, S.S.: Integer representations towards efficient counting in the bit probe model. In: Ogihara, M., Tarui, J. (eds.) TAMC 2011. LNCS, vol. 6648, pp. 206–217. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Brodal, G.S., Venkatesh, S.: Improved bounds for dictionary look-up with one error. Information Processing Letters 75(1), 57–59 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Broder, A., Mitzenmacher, M.: Network applications of bloom filters: A survey. Internet Mathematics 1(4), 485–509 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Brodnik, A., Munro, J.I.: Membership in constant time and almost-minimum space. SIAM Journal on Computing 28(5), 1627–1640 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  11. Buhrman, H., Miltersen, P.B., Radhakrishnan, J., Venkatesh, S.: Are bitvectors optimal? SIAM Journal on Computing 31(6), 1723–1744 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Clancy, M.J., Knuth, D.E.: A programming and problem-solving seminar. Tech. rep., Stanford, CA, USA (1977)

    Google Scholar 

  13. Demaine, E.D., López-Ortiz, A.: A linear lower bound on index size for text retrieval. Journal of Algorithms 48(1), 2–15 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dodis, Y., Pǎtraşcu, M., Thorup, M.: Changing base without losing space. In: Proceedings of the 42nd ACM Symposium on Theory of Computing, pp. 593–602. ACM (2010)

    Google Scholar 

  15. Elias, P., Flower, R.A.: The complexity of some simple retrieval problems. Journal of the ACM (JACM) 22(3), 367–379 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  16. Elmasry, A., Jensen, C., Katajainen, J.: Two skew-binary numeral systems and one application. Theory Comput. Syst. 50(1), 185–211 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Frandsen, G.S., Miltersen, P.B., Skyum, S.: Dynamic word problems. J. ACM 44(2), 257–271 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  18. Fredman, M.L.: Observations on the complexity of generating quasi-Gray codes. SIAM Journal on Computing 7(2), 134–146 (1978)

    Article  MathSciNet  Google Scholar 

  19. Fredman, M.L., Komlós, J., Szemerédi, E.: Storing a sparse table with 0(1) worst case access time. Journal of the ACM (JACM) 31(3), 538–544 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  20. Fredman, M.: The complexity of maintaining an array and computing its partial sums. J. ACM 29(1), 250–260 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  21. Gál, A., Miltersen, P.B.: The cell probe complexity of succinct data structures. Theor. Comput. Sci. 379(3), 405–417 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  22. Giora, Y., Kaplan, H.: Optimal dynamic vertical ray shooting in rectilinear planar subdivisions. ACM Transactions on Algorithms 5(3), 28:1–28:51 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Golynski, A.: Optimal lower bounds for rank and select indexes. Theoretical Computer Science 387(3), 348–359 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Golynski, A., Orlandi, A., Raman, R., Rao, S.S.: Optimal indexes for sparse bit vectors. Algorithmica, 1–19 (2011)

    Google Scholar 

  25. Gray, F.: Pulse code communications. U.S. Patent (2632058) (1953)

    Google Scholar 

  26. Jansens, D.: Improved Methods for Generating Quasi-Gray Codes. Master’s thesis, School of Computer Science, Carleton University (April 2010)

    Google Scholar 

  27. Knuth, D.E.: Sorting and searching: The art of computer programming III. Addison-Wesley, Reading (1973)

    MATH  Google Scholar 

  28. Knuth, D.E.: The Art of Computer Programming. Fascicle 2: Generating All Tuples and Permutations (Art of Computer Programming), vol. 4. Addison-Wesley Professional (2005)

    Google Scholar 

  29. Lewenstein, M., Munro, J.I., Nicholson, P.K., Raman, V.: Explicit data structures in the bitprobe model (submitted manuscript, 2013)

    Google Scholar 

  30. Miltersen, P.B.: The bit probe complexity measure revisited. In: Enjalbert, P., Wagner, K.W., Finkel, A. (eds.) STACS 1993. LNCS, vol. 665, pp. 662–671. Springer, Heidelberg (1993), http://portal.acm.org/citation.cfm?id=646509.694667

    Chapter  Google Scholar 

  31. Minsky, M.L., Papert, S.: Perceptrons: An Introduction to Computational Geometry. The MIT Press (1969)

    Google Scholar 

  32. Mortensen, C.W., Pagh, R., Patrascu, M.: On dynamic range reporting in one dimension. In: Gabow, H.N., Fagin, R. (eds.) STOC, pp. 104–111. ACM (2005)

    Google Scholar 

  33. Nisan, N., Wigderson, A.: Hardness vs randomness. Journal of Computer and System Sciences 49(2), 149–167 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  34. Okasaki, C.: Purely functional data structures. Cambridge University Press (1999)

    Google Scholar 

  35. Pagh, A., Pagh, R., Rao, S.S.: An optimal bloom filter replacement. In: SODA, pp. 823–829. SIAM (2005)

    Google Scholar 

  36. Pagh, R.: Low redundancy in static dictionaries with constant query time. SIAM Journal on Computing 31(2), 353–363 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  37. Pagh, R.: On the cell probe complexity of membership and perfect hashing. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, STOC 2001, pp. 425–432. ACM, New York (2001)

    Google Scholar 

  38. Pǎtraşcu, M.: Succincter. In: Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science, pp. 305–313. IEEE Computer Society (2008)

    Google Scholar 

  39. Pǎtraşcu, M., Tarniţǎ, C.E.: On dynamic bit-probe complexity. Theoretical Computer Science 380(1), 127–142 (2007)

    MathSciNet  MATH  Google Scholar 

  40. Radhakrishnan, J., Raman, V., Rao, S.S.: Explicit deterministic constructions for membership in the bitprobe model. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 290–299. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  41. Radhakrishnan, J., Shah, S., Shannigrahi, S.: Data structures for storing small sets in the bitprobe model. In: de Berg, M., Meyer, U. (eds.) ESA 2010, Part II. LNCS, vol. 6347, pp. 159–170. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  42. Rahman, M.Z.: Data Structuring Problems in the Bit Probe Model. Master’s thesis, University of Waterloo (2007)

    Google Scholar 

  43. Rahman, M.Z., Munro, J.I.: Integer representation and counting in the bit probe model. Algorithmica 56(1), 105–127 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  44. Rao, S.S.: Succinct Data Structures. Ph.D. thesis, Institute of Mathematical Sciences (2001)

    Google Scholar 

  45. Savage, C.: A survey of combinatorial Gray codes. SIAM Review 39, 605–629 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  46. Ta-Shma, A.: Storing information with extractors. Information Processing Letters 83(5), 267–274 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  47. Tao, T., Croot III., E., Helfgott, H.: Deterministic methods to find primes. Mathematics of Computation 81(278), 1233–1246 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  48. Viola, E.: Bit-probe lower bounds for succinct data structures. SIAM Journal on Computing 41(6), 1593–1604 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  49. Vuillemin, J.: A data structure for manipulating priority queues. Commun. ACM 21(4), 309–315 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  50. Yao, A.C.: Should tables be sorted? J. ACM 28(3), 615–628 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  51. Yao, A.C., Yao, F.F.: Dictionary look-up with one error. Journal of Algorithms 25(1), 194–202 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Cheriton School of Computer Science, University of Waterloo, Canada

    Patrick K. Nicholson

  2. School of Computer Science and Engineering, Seoul National University, Republic of Korea

    S. Srinivasa Rao

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  1. Patrick K. Nicholson
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  2. Venkatesh Raman
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  3. S. Srinivasa Rao
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Editor information

Editors and Affiliations

  1. Faculty of Computer and Information Science, University of Ljubljana, Ljubljana, Slovenia

    Andrej Brodnik

  2. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada

    Alejandro López-Ortiz

  3. The Institute of Mathematical Sciences, Chennai, India

    Venkatesh Raman

  4. Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay

    Alfredo Viola

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Nicholson, P.K., Raman, V., Rao, S.S. (2013). A Survey of Data Structures in the Bitprobe Model. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds) Space-Efficient Data Structures, Streams, and Algorithms. Lecture Notes in Computer Science, vol 8066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40273-9_19

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  • DOI: https://doi.org/10.1007/978-3-642-40273-9_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40272-2

  • Online ISBN: 978-3-642-40273-9

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