Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
429968 | Journal of Computer and System Sciences | 2016 | 15 Pages |
•Binary matrices solvable for small range of Hamming distances, NP-hard otherwise.•Sunflowers as combinatorial tool for structural matrix analysis.•FPT and W-hardness for general matrices.
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⌉+1H≤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.