2 research outputs found
A Double Exponential Lower Bound for the Distinct Vectors Problem
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
A Double Exponential Lower Bound for the Distinct Vectors Problem
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