Exploiting Hidden Structure in Selecting Dimensions that Distinguish Vectors

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.

Accepted for publication in Journal of Computer and System Sciences (Elsevier)

Cited by in corpus (3)

• Optimal-size problem kernels for $d$-Hitting Set in linear time and space
• Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU
• A Double Exponential Lower Bound for the Distinct Vectors Problem