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arXiv · 2203.09334

Stronger 3SUM-Indexing Lower Bounds

Eldon Chung·Kasper Green Larsen
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Abstract

The $3$SUM-Indexing problem was introduced as a data structure version of the $3$SUM problem, with the goal of proving strong conditional lower bounds for static data structures via reductions. Ideally, the conjectured hardness of $3$SUM-Indexing should be replaced by an unconditional lower bound. Unfortunately, we are far from proving this, with the strongest current lower bound being a logarithmic query time lower bound by Golovnev et al. from STOC'20. Moreover, their lower bound holds only for non-adaptive data structures and they explicitly asked for a lower bound for adaptive data structures. Our main contribution is precisely such a lower bound against adaptive data structures. As a secondary result, we also strengthen the non-adaptive lower bound of Golovnev et al. and prove strong lower bounds for $2$-bit-probe non-adaptive $3$SUM-Indexing data structures via a completely new approach that we find interesting in its own right.

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Eldon Chung, Kasper Green Larsen. 2022-03-17. Stronger 3SUM-Indexing Lower Bounds. https://doi.org/10.1137/1.9781611977554.ch19

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