Authors: Marcin Pilipczuk ; Manuel Sorge

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.

• 68Q17 - Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
• 68Q27 - Parameterized complexity, tractability and kernelization
• 68T05 - Learning and adaptive systems in artificial intelligence