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Space Complexity of Two Adaptive Bitprobe Schemes Storing Three Elements

Author Deepanjan Kesh

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ACM Subject Classification
  • Information systems → Data structures
Keywords
  • Data structures
  • set membership problem
  • bitprobe model
  • lower bound

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Abstract

We consider the following set membership problem in the bitprobe model - that of storing subsets of size at most three from a universe of size m, and answering membership queries using two adaptive bitprobes. Baig and Kesh [Mirza Galib Anwarul Husain Baig and Deepanjan Kesh, 2018] proposed a scheme for the problem which takes O(m^{2/3}) space. In this paper, we present a proof which shows that any scheme for the problem requires Omega(m^{2/3}) amount of space. These two results together settle the space complexity issue for this particular problem.

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Deepanjan Kesh. Space Complexity of Two Adaptive Bitprobe Schemes Storing Three Elements. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 12:1-12:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.FSTTCS.2018.12

Author Details

Deepanjan Kesh
  • Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India

References

  1. Noga Alon and Uriel Feige. On the power of two, three and four probes. In Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2009, New York, NY, USA, January 4-6, 2009, pages 346-354, 2009. Google Scholar
  2. Mirza Galib Anwarul Husain Baig and Deepanjan Kesh. Two New Schemes in the Bitprobe Model. In WALCOM: Algorithms and Computation - 12th International Conference, WALCOM 2018, Dhaka, Bangladesh, March 3-5, 2018, Proceedings, pages 68-79, 2018. Google Scholar
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  7. Jaikumar Radhakrishnan, Smit Shah, and Saswata Shannigrahi. Data Structures for Storing Small Sets in the Bitprobe Model. In Algorithms - ESA 2010, 18th Annual European Symposium, Liverpool, UK, September 6-8, 2010. Proceedings, Part II, pages 159-170, 2010. Google Scholar
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