## Abstract

The NP-hard Distinct Vectors problem asks to delete as many columns as possible from a matrix such that all rows in the resulting matrix are still pairwise distinct. Our main result is that, for binary matrices, there is a complexity dichotomy for Distinct Vectors based on the maximum (H) and the minimum (h) pairwise Hamming distance between matrix rows: Distinct Vectors can be solved in polynomial time if H≤2[h/2]+1, and is NP-complete otherwise. Moreover, we explore connections of Distinct Vectors to hitting sets, thereby providing several fixed-parameter tractability and intractability results also for general matrices.

Original language | English |
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Pages (from-to) | 521-535 |

Number of pages | 15 |

Journal | Journal of Computer and System Sciences |

Volume | 82 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 2016 |

## Keywords

- Combinatorial feature selection
- Combinatorics of binary matrices
- Dimension reduction
- Fixed-parameter tractability
- Machine learning
- Minimal reduct problem
- NP-hardness
- W-hardness
- Δ-Systems