The Strong 3SUMINDEXING Conjecture is False
Abstract
In the 3SUMIndexing 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 3SUMIndexing which uses $n^{2\Omega(1)}$ space and $n^{1\Omega(1)}$ query time. We show that the conjecture is false by reducing the 3SUMIndexing problem to the problem of inverting functions, and then applying an algorithm of Fiat and Naor [SICOMP'1999] for inverting functions.
 Publication:

arXiv eprints
 Pub Date:
 July 2019
 arXiv:
 arXiv:1907.11206
 Bibcode:
 2019arXiv190711206K
 Keywords:

 Computer Science  Data Structures and Algorithms