The Strong 3SUM-INDEXING Conjecture is False

07/25/2019

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by   Tsvi Kopelowitz, et al.

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In the 3SUM-Indexing problem the goal is to preprocess two lists of elements from U, A=(a_1,a_2,...,a_n) and B=(b_1,b_2,...,b_n), such that given an element c∈ U one can quickly determine whether there exists a pair (a,b)∈ A × B where a+b=c. Goldstein et al. [WADS'2017] conjectured that there is no algorithm for 3SUM-Indexing which uses n^2-Ω(1) space and n^1-Ω(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.