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arXiv · 1512.01150

Exploiting Hidden Structure in Selecting Dimensions that Distinguish Vectors

Vincent Froese·René van Bevern·Rolf Niedermeier·Manuel Sorge
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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 ceil(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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Vincent Froese, René van Bevern, Rolf Niedermeier, Manuel Sorge. 2015-12-03. Exploiting Hidden Structure in Selecting Dimensions that Distinguish Vectors. https://doi.org/10.1016/j.jcss.2015.11.011

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