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Space-Efficient B Trees via Load-Balancing

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Combinatorial Algorithms (IWOCA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13270))

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Abstract

We study succinct variants of B trees in the word RAM model that require \(s + o(s)\) bits of space, where s is the number of bits essentially needed for storing keys and possibly other satellite values. Assuming that elements are sorted by keys (not necessarily in the order of their integer representations), our B trees support standard operations such as searching, insertion and deletion of elements. In some applications it is useful to associate a satellite value to each element, and to support aggregate operations such as computing the sum of values, the minimum/maximum value in a given range, or search operations based on those values. We propose a B tree representation storing n elements in \(s + \mathop {}\mathopen {}\mathcal {O}\mathopen {}(s / \lg n)\) bits of space and supporting all mentioned operations in \(\mathop {}\mathopen {}\mathcal {O}\mathopen {}(\lg n)\) time.

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Notes

  1. 1.

    Note that if all keys are distinct, then \(k \ge \lg n\) by the pigeonhole principle.

  2. 2.

    More precisely, these blocks were valid at least before the enlargement of \(B_i\), which could have triggered a shifting that invalidated either \(B_{i-1}\) or \(B_{i+1}\).

References

  1. Bayer, R., McCreight, E.M.: Organization and maintenance of large ordered indexes. In: Proceedings of the SIGFIDET, pp. 107–141 (1970)

    Google Scholar 

  2. Bille, P., et al.: Dynamic relative compression, dynamic partial sums, and substring concatenation. Algorithmica 80(11), 3207–3224 (2018)

    Article  MathSciNet  Google Scholar 

  3. Blandford, D.K., Blelloch, G.E.: Compact representations of ordered sets. In: Proceedings of the SODA, pp. 11–19 (2004)

    Google Scholar 

  4. Comer, D.: The ubiquitous B-tree. ACM Comput. Surv. 11(2), 121–137 (1979)

    Article  MathSciNet  Google Scholar 

  5. Delpratt, O.N., Rahman, N., Raman, R.: Compressed prefix sums. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 235–247. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-69507-3_19

    Chapter  Google Scholar 

  6. Dietz, P.F.: Optimal algorithms for list indexing and subset rank. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1989. LNCS, vol. 382, pp. 39–46. Springer, Heidelberg (1989). https://doi.org/10.1007/3-540-51542-9_5

    Chapter  MATH  Google Scholar 

  7. Elias, P.: Efficient storage and retrieval by content and address of static files. J. ACM 21(2), 246–260 (1974)

    Article  MathSciNet  Google Scholar 

  8. Farzan, A., Munro, J.I.: Succinct representation of dynamic trees. Theor. Comput. Sci. 412(24), 2668–2678 (2011)

    Article  MathSciNet  Google Scholar 

  9. Ferragina, P., Grossi, R.: The string B-tree: a new data structure for string search in external memory and its applications. J. ACM 46(2), 236–280 (1999)

    Article  MathSciNet  Google Scholar 

  10. Franceschini, G., Grossi, R.: Optimal implicit dictionaries over unbounded universes. Theory Comput. Syst. 39(2), 321–345 (2006)

    Article  MathSciNet  Google Scholar 

  11. González, R., Navarro, G.: Rank/select on dynamic compressed sequences and applications. Theor. Comput. Sci. 410(43), 4414–4422 (2009)

    Article  MathSciNet  Google Scholar 

  12. Graefe, G.: Modern B-tree techniques. Found. Trends Databases 3(4), 203–402 (2011)

    Article  Google Scholar 

  13. He, M., Munro, J.I.: Succinct representations of dynamic strings. In: Chavez, E., Lonardi, S. (eds.) SPIRE 2010. LNCS, vol. 6393, pp. 334–346. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16321-0_35

    Chapter  Google Scholar 

  14. Jesus, P., Baquero, C., Almeida, P.S.: A survey of distributed data aggregation algorithms. IEEE Commun. Surv. Tutor. 17(1), 381–404 (2015)

    Article  Google Scholar 

  15. Katajainen, J., Rao, S.S.: A compact data structure for representing a dynamic multiset. Inf. Process. Lett. 110(23), 1061–1066 (2010)

    Article  MathSciNet  Google Scholar 

  16. Knuth, D.E.: The Art of Computer Programming, Volume 3: Sorting and Searching. Addison Wesley, Redwood City (1998)

    Google Scholar 

  17. Munro, J.I., Nekrich, Y.: Compressed data structures for dynamic sequences. In: Bansal, N., Finocchi, I. (eds.) ESA 2015. LNCS, vol. 9294, pp. 891–902. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48350-3_74

    Chapter  Google Scholar 

  18. Navarro, G., Nekrich, Y.: Optimal dynamic sequence representations. SIAM J. Comput. 43(5), 1781–1806 (2014)

    Article  MathSciNet  Google Scholar 

  19. Prezza, N.: A framework of dynamic data structures for string processing. In: Proceedings of the SEA. LIPIcs, vol. 75, pp. 11:1–11:15 (2017)

    Google Scholar 

  20. Raman, R., Rao, S.S.: Succinct dynamic dictionaries and trees. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 357–368. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-45061-0_30

    Chapter  MATH  Google Scholar 

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Acknowledgment

This work was supported by JSPS KAKENHI Grant Numbers JP19K20213 (TI), JP21K17701 and JP21H05847 (DK).

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Authors and Affiliations

  1. M&D Data Science Center, Tokyo Medical and Dental University, Bunkyo City, Japan

    Dominik Köppl

  2. Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, Japan

    Tomohiro I

Authors
  1. Tomohiro I
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  2. Dominik Köppl
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Correspondence to Dominik Köppl .

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Editors and Affiliations

  1. Université Paris-Dauphine, Paris, France

    Cristina Bazgan

  2. Universität Trier, Trier, Germany

    Henning Fernau

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I, T., Köppl, D. (2022). Space-Efficient B Trees via Load-Balancing. In: Bazgan, C., Fernau, H. (eds) Combinatorial Algorithms. IWOCA 2022. Lecture Notes in Computer Science, vol 13270. Springer, Cham. https://doi.org/10.1007/978-3-031-06678-8_24

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  • DOI: https://doi.org/10.1007/978-3-031-06678-8_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-06677-1

  • Online ISBN: 978-3-031-06678-8

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