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Lower Bounds for Semi-adaptive Data Structures via Corruption

Authors Pavel Dvořák, Bruno Loff



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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

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