A Double Exponential Lower Bound for the Distinct Vectors Problem
Computational Complexity
2023-06-22 v3 Discrete Mathematics
Abstract
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.
Cite
@article{arxiv.2002.01293,
title = {A Double Exponential Lower Bound for the Distinct Vectors Problem},
author = {Marcin Pilipczuk and Manuel Sorge},
journal= {arXiv preprint arXiv:2002.01293},
year = {2023}
}