Lower Bounds for Semi-adaptive Data Structures via Corruption

Authors Pavel Dvořák, Bruno Loff



PDF
Thumbnail PDF

File

LIPIcs.FSTTCS.2020.20.pdf
  • Filesize: 0.52 MB
  • 15 pages

Document Identifiers

Author Details

Pavel Dvořák
  • Charles University, Prague, Czech Republic
Bruno Loff
  • INESC-Tec and University of Porto, Portugal

Acknowledgements

We would like to thank Michal Koucký, who worked with us on this paper until the coronavirus pandemic forced him busily away. We would also like to thank Arkadev Chattopadhyay for helpful pointers.

Cite AsGet BibTex

Pavel Dvořák and Bruno Loff. Lower Bounds for Semi-adaptive Data Structures via Corruption. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.FSTTCS.2020.20

Abstract

In a dynamic data structure problem we wish to maintain an encoding of some data in memory, in such a way that we may efficiently carry out a sequence of queries and updates to the data. A long-standing open problem in this area is to prove an unconditional polynomial lower bound of a trade-off between the update time and the query time of an adaptive dynamic data structure computing some explicit function. Ko and Weinstein provided such lower bound for a restricted class of semi-adaptive data structures, which compute the Disjointness function. There, the data are subsets x₁,… ,x_k and y of {1,… ,n}, the updates can modify y (by inserting and removing elements), and the queries are an index i ∈ {1,… ,k} (query i should answer whether x_i and y are disjoint, i.e., it should compute the Disjointness function applied to (x_i, y)). The semi-adaptiveness places a restriction in how the data structure can be accessed in order to answer a query. We generalize the lower bound of Ko and Weinstein to work not just for the Disjointness, but for any function having high complexity under the smooth corruption bound.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • semi-adaptive dynamic data structure
  • polynomial lower bound
  • corruption bound
  • information theory

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Amir Abboud and Virginia Vassilevska Williams. Popular conjectures imply strong lower bounds for dynamic problems. In Proceedings of the 55th FOCS, pages 434-443, 2014. Google Scholar
  2. Laszlo Babai, Peter Frankl, and Janos Simon. Complexity classes in communication complexity theory. In Proceedings of the 27th FOCS, page 337–347, 1986. Google Scholar
  3. Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. An information statistics approach to data stream and communication complexity. In Proceedings of the 43rd FOCS, page 209–218, 2002. Google Scholar
  4. Paul Beame, Toniann Pitassi, Nathan Segerlind, and Avi Wigderson. A strong direct product theorem for corruption and the multiparty communication complexity of disjointness. Computational Complexity, 15(4):391–432, 2006. Google Scholar
  5. Amit Chakrabarti, Ranganath Kondapally, and Zhenghui Wang. Information complexity versus corruption and applications to orthogonality and gap-hamming. In Proceedings of the 16th RANDOM, pages 483-494. Springer, 2012. Google Scholar
  6. Arkadev Chattopadhyay, Jeff Edmonds, Faith Ellen, and Toniann Pitassi. A Little Advice Can Be Very Helpful. In Proceedings of the 23rd SODA, pages 615-625, 2012. Google Scholar
  7. Thomas M. Cover and Joy A. Thomas. Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing). Wiley-Interscience, 2006. Google Scholar
  8. Michael Fredman and Michael Saks. The cell probe complexity of dynamic data structures. In Proceedings of the 21st STOC, pages 345-354, 1989. Google Scholar
  9. Rahul Jain and Hartmut Klauck. The partition bound for classical communication complexity and query complexity. In Proceedings of the 25th CCC, page 247–258, 2010. Google Scholar
  10. Bala Kalyanasundaram and Georg Schintger. The Probabilistic Communication Complexity of Set Intersection. SIAM Journal of Discrete Mathematics, 5(4):545-557, 1992. Google Scholar
  11. Young Kun Ko and Omri Weinstein. An Adaptive Step Toward the Multiphase Conjecture, 2019. URL: http://arxiv.org/abs/1910.13543.
  12. Eyal Kushilevitz and Noam Nisan. Communication Complexity. Cambridge University Press, 1996. Google Scholar
  13. Kasper Green Larsen. The cell probe complexity of dynamic range counting. In Proceedings of the 44th STOC, pages 85-94, 2012. Google Scholar
  14. Kasper Green Larsen, Omri Weinstein, and Huacheng Yu. Crossing the logarithmic barrier for dynamic boolean data structure lower bounds. SIAM Journal on Computing, 2020. Google Scholar
  15. Mihai Păatraşcu and Erik D Demaine. Tight bounds for the partial-sums problem. In Proceedings of the 15th SODA, pages 20-29, 2004. Google Scholar
  16. Mihai Patrascu. Towards polynomial lower bounds for dynamic problems. In Proceedings of the 42nd STOC, pages 603-610, 2010. Google Scholar
  17. Mihai Patrascu and Erik D Demaine. Logarithmic lower bounds in the cell-probe model. SIAM Journal on Computing, 35(4):932-963, 2006. Google Scholar
  18. Mihai Pătraşcu. Towards Polynomial Lower Bounds for Dynamic Problems. In Proceedings of the 42nd STOC, pages 603-610, 2010. Google Scholar
  19. Alexander A. Razborov. On the distributional complexity of disjointness. Theoretical Computer Science, 106:385-390, 1992. Google Scholar
  20. Alexander A Sherstov. The communication complexity of gap hamming distance. Theory of Computing, 8(1):197-208, 2012. Google Scholar
  21. Andrew Chi-Chih Yao. Some complexity questions related to distributive computing (preliminary report). In Proceedings of the 11h STOC, pages 209-213, 1979. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail