The Strong 3SUM-INDEXING Conjecture is False
Tsvi Kopelowitz, Ely Porat

TL;DR
This paper disproves the Strong 3SUM-INDEXING Conjecture by reducing the problem to function inversion and applying a known algorithm, showing more efficient solutions are possible.
Contribution
It demonstrates that the longstanding conjecture about the hardness of 3SUM-Indexing is false through a novel reduction and application of existing function inversion algorithms.
Findings
The conjecture that 3SUM-Indexing cannot be solved with certain space and time bounds is false.
A reduction from 3SUM-Indexing to function inversion is established.
An existing function inversion algorithm can be used to solve 3SUM-Indexing efficiently.
Abstract
In the 3SUM-Indexing problem the goal is to preprocess two lists of elements from , and , such that given an element one can quickly determine whether there exists a pair where . Goldstein et al.~[WADS'2017] conjectured that there is no algorithm for 3SUM-Indexing which uses space and query time. We show that the conjecture is false by reducing the 3SUM-Indexing problem to the problem of inverting functions, and then applying an algorithm of Fiat and Naor [SICOMP'1999] for inverting functions.
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Taxonomy
TopicsAlgorithms and Data Compression · semigroups and automata theory · graph theory and CDMA systems
