Compressed Persistent Index for Efficient Rank/Select Queries

  • Wing-Kai Hon
  • Lap-Kei Lee
  • Kunihiko Sadakane
  • Konstantinos Tsakalidis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)

Abstract

We design compressed persistent indices that store a bit vector of size n and support a sequence of k bit-flip update operations, such that rank and select queries at any version can be supported efficiently. In particular, we present partially and fully persistent compressed indices for offline and online updates that support all operations in time polylogarithmic in n and k. This improves upon the space or time complexities of straightforward approaches, when \(k=O(\frac{n}{\log n})\), which is common in biological applications. We also prove that any partially persistent index that occupies O((n + k)log(nk)) bits requires ω(1) time to support the rank query at a given version.

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References

  1. 1.
    Brodal, G.S., Sioutas, S., Tsakalidis, K., Tsichlas, K.: Fully persistent B-trees. In: Proc. SODA, pp. 602–614 (2012)Google Scholar
  2. 2.
    Cole, R., Gottlieb, L.A., Lewenstein, M.: Dictionary matching and indexing with errors and don’t cares. In: Proc. STOC, pp. 91–100 (2004)Google Scholar
  3. 3.
    Dietz, P.F.: Fully Persistent arrays. In: Dehne, F., Santoro, N., Sack, J.-R. (eds.) WADS 1989. LNCS, vol. 382, pp. 67–74. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  4. 4.
    Driscoll, J.R., Sarnak, N., Sleator, D.D., Tarjan, R.E.: Making data structures persistent. J. Comput. Syst. Sci. 38(1), 86–124 (1989)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Ferragina, P., Manzini, G.: Opportunistic data structures with applications. In: Proc. FOCS, pp. 390–398 (2000)Google Scholar
  6. 6.
    Grossi, R., Gupta, A., Vitter, J.S.: High-order entropy-compressed text indexes. In: Proc. SODA, pp. 841–850 (2003)Google Scholar
  7. 7.
    JáJá, J., Mortensen, C.W., Shi, Q.: Space-efficient and fast algorithms for multidimensional dominance reporting and counting. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 558–568. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Kaplan, H.: Persistent data structures. In: Handbook on Data Structures and Applications, ch. 31, pp. 31-1–31-26. CRC Press (2004)Google Scholar
  9. 9.
    Kopelowitz, T.: On-line indexing for general alphabets via predecessor queries on subsets of an ordered list. In: Proc. FOCS, pp. 283–292 (2012)Google Scholar
  10. 10.
    Mäkinen, V., Navarro, G., Sirén, J., Välimäki, N.: Storage and retrieval of highly repetitive sequence collections. J. Comp. Biology 17(3), 281–308 (2010)CrossRefGoogle Scholar
  11. 11.
    Nekrich, Y.: Orthogonal range searching in linear and almost-linear space. Comput. Geom. 42(4), 342–351 (2009)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Pǎtraşcu, M.: Lower bounds for 2-dimensional range counting. In: Proc. STOC, pp. 40–46 (2007)Google Scholar
  13. 13.
    Raman, R., Raman, V., Satti, S.R.: Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets. ACM Transactions on Algorithms 3(4), 43 (2007)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Sadakane, K., Navarro, G.: Fully-functional succinct trees. In: Proc. SODA, pp. 134–149 (2010)Google Scholar
  15. 15.
    The 1000 Genomes Project Consortium. A map of human genome variation from population-scale sequencing. Nature 467(7319), 1061–1073 (2010)Google Scholar
  16. 16.
    Willard, D.E.: Log-logarithmic worst-case range queries are possible in space Θ(n). Information Processing Letters 17(2), 81–84 (1983)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Wing-Kai Hon
    • 1
  • Lap-Kei Lee
    • 2
  • Kunihiko Sadakane
    • 3
  • Konstantinos Tsakalidis
    • 4
  1. 1.Department of Computer ScienceNational Tsing Hua UniversityTaiwan
  2. 2.HKU-BGI Bioinformatics Algorithms & Core Technology Research LaboratoryUniversity of Hong KongHong Kong
  3. 3.National Institute of InformaticsTokyoJapan
  4. 4.Department of Computer Science & EngineeringHKUSTHong Kong

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