Geodesic
A Double Exponential Lower Bound for the Distinct Vectors Problem
Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 4.

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In the (binary) Distinct Vectors problem we are given a binary matrix A with pairwise different rows and want to select at most k columns such that, restricting the matrix to these columns, all rows are still pairwise different. A result by Froese et al. [JCSS] implies a 2^2^(O(k)) * poly(|A|)-time brute-force algorithm for Distinct Vectors. We show that this running time bound is essentially optimal by showing that there is a constant c such that the existence of an algorithm solving Distinct Vectors with running time 2^(O(2^(ck))) * poly(|A|) would contradict the Exponential Time Hypothesis.
DOI : 10.23638/DMTCS-22-4-7
Classification : 68Q17, 68Q27, 68T05 
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Pilipczuk, Marcin; Sorge, Manuel. A Double Exponential Lower Bound for the Distinct Vectors Problem. Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 4. doi : 10.23638/DMTCS-22-4-7. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-4-7/

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