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arXiv · 2211.14664

Lower Bounds on Retroactive Data Structures

Lily Chung·Erik D. Demaine·Dylan Hendrickson·Jayson Lynch
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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 $T(n,m) \cdot m^{1-o(1)}$ 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 $O(T(n,m) \cdot m)$ time per operation, so our lower bound is tight up to an $m^{o(1)}$ factor common in fine-grained complexity.

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Lily Chung, Erik D. Demaine, Dylan Hendrickson, Jayson Lynch. 2022-11-26. Lower Bounds on Retroactive Data Structures. https://arxiv.org/abs/2211.14664

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