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Lower Bounds on Retroactive Data Structures

Authors Lily Chung , Erik D. Demaine , Dylan Hendrickson , Jayson Lynch

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Lily Chung
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Erik D. Demaine
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Dylan Hendrickson
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Jayson Lynch
  • Cheriton School of Computer Science, University of Waterloo, Canada

Acknowledgements

This work was initiated during open problem solving in the MIT class on Advanced Data Structures (6.851) in Spring 2021. We thank the other participants of that class - in particular, Joshua Ani, Josh Brunner, and Naveen Venkat - for related discussions and providing an inspiring atmosphere. We also thank Michael Coulombe for helpful pointers regarding time travel.

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Lily Chung, Erik D. Demaine, Dylan Hendrickson, and Jayson Lynch. Lower Bounds on Retroactive Data Structures. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 32:1-32:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ISAAC.2022.32

Abstract

We prove essentially optimal fine-grained lower bounds on the gap between a data structure and a partially retroactive version of the same data structure. Precisely, assuming any one of three standard conjectures, we describe a problem that has a data structure where operations run in O(T(n,m)) time per operation, but any partially retroactive version of that data structure requires T(n,m)⋅m^{1-o(1)} worst-case time per operation, where n is the size of the data structure at any time and m is the number of operations. Any data structure with operations running in O(T(n,m)) time per operation can be converted (via the "rollback method") into a partially retroactive data structure running in O(T(n,m)⋅m) time per operation, so our lower bound is tight up to an m^o(1) factor common in fine-grained complexity.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cell probe models and lower bounds
Keywords
  • Retroactivity
  • time travel
  • rollback
  • fine-grained complexity

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