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arXiv · 1907.11206

The Strong 3SUM-INDEXING Conjecture is False

Tsvi Kopelowitz·Ely Porat
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Abstract

In the 3SUM-Indexing problem the goal is to preprocess two lists of elements from $U$, $A=(a_1,a_2,\ldots,a_n)$ and $B=(b_1,b_2,...,b_n)$, such that given an element $c\in U$ one can quickly determine whether there exists a pair $(a,b)\in A \times B$ where $a+b=c$. Goldstein et al.~[WADS'2017] conjectured that there is no algorithm for 3SUM-Indexing which uses $n^{2-\Omega(1)}$ space and $n^{1-\Omega(1)}$ 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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Tsvi Kopelowitz, Ely Porat. 2019-07-25. The Strong 3SUM-INDEXING Conjecture is False. https://arxiv.org/abs/1907.11206

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