Exploiting hidden structure in selecting dimensions that distinguish vectors. Froese, V., van Bevern, R., Niedermeier, R., & Sorge, M. *Journal of Computer and System Sciences*, 82(3):521–535, 2016.

Preprint doi abstract bibtex

Preprint doi abstract bibtex

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.

@article{FBNS16, title = {Exploiting hidden structure in selecting dimensions that distinguish vectors}, author = {Vincent Froese and René van Bevern and Rolf Niedermeier and Manuel Sorge}, url_Preprint = {http://arxiv.org/abs/1512.01150}, doi = {10.1016/j.jcss.2015.11.011}, issn = {0022-0000}, year = 2016, date = {2016-05-01}, journal = {Journal of Computer and System Sciences}, volume = 82, number = 3, pages = {521--535}, 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.} }

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