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Data Structures Lower Bounds and Popular Conjectures

Authors Pavel Dvořák, Michal Koucký, Karel Král, Veronika Slívová

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ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • Data structures
  • Circuits
  • Lower bounds
  • Network Coding Conjecture

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Abstract

In this paper, we investigate the relative power of several conjectures that attracted recently lot of interest. We establish a connection between the Network Coding Conjecture (NCC) of Li and Li [Li and Li, 2004] and several data structure problems such as non-adaptive function inversion of Hellman [M. Hellman, 1980] and the well-studied problem of polynomial evaluation and interpolation. In turn these data structure problems imply super-linear circuit lower bounds for explicit functions such as integer sorting and multi-point polynomial evaluation.

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Pavel Dvořák, Michal Koucký, Karel Král, and Veronika Slívová. Data Structures Lower Bounds and Popular Conjectures. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 39:1-39:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ESA.2021.39

Author Details

Pavel Dvořák
  • Charles University, Prague, Czech Republic
Michal Koucký
  • Charles University, Prague, Czech Republic
Karel Král
  • Charles University, Prague, Czech Republic
Veronika Slívová
  • Charles University, Prague, Czech Republic

Funding

The authors were partially supported by Czech Science Foundation GAČR grant #19-27871X. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 823748. The fourth author was supported by Charles University project UNCE/SCI/004.

Acknowledgements

We would like to thank to Mike Saks and Sagnik Mukhopadhyay for insightful discussions.

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