Stronger 3SUM-Indexing Lower Bounds
Eldon Chung, Kasper Green Larsen

TL;DR
This paper establishes new strong lower bounds for the 3SUM-Indexing problem, including the first adaptive data structure lower bounds and improved bounds for non-adaptive cases, advancing understanding of its computational hardness.
Contribution
It provides the first lower bounds for adaptive data structures for 3SUM-Indexing and strengthens existing bounds for non-adaptive data structures using a novel approach.
Findings
First adaptive data structure lower bounds for 3SUM-Indexing.
Strengthened non-adaptive lower bounds for 2-bit probes.
New techniques for proving data structure lower bounds.
Abstract
The SUM-Indexing problem was introduced as a data structure version of the SUM problem, with the goal of proving strong conditional lower bounds for static data structures via reductions. Ideally, the conjectured hardness of 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 -bit-probe non-adaptive SUM-Indexing data structures via a completely new…
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Taxonomy
TopicsAlgorithms and Data Compression · Artificial Intelligence in Games · Data Management and Algorithms
