Exploiting hidden structure in selecting dimensions that distinguish vectors

Vincent Froese; René Van Bevern; Rolf Niedermeier; Manuel Sorge

doi:10.1016/j.jcss.2015.11.011

Exploiting hidden structure in selecting dimensions that distinguish vectors

Vincent Froese, René Van Bevern, Rolf Niedermeier, Manuel Sorge

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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
Pages (from-to)	521-535
Number of pages	15
Journal	Journal of Computer and System Sciences
Volume	82
Issue number	3
DOIs	https://doi.org/10.1016/j.jcss.2015.11.011
State	Published - 1 Jan 2016
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1016/j.jcss.2015.11.011

Cite this

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title = "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[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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AU - Froese, Vincent

AU - Van Bevern, René

AU - Niedermeier, Rolf

AU - Sorge, Manuel

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Y1 - 2016/1/1

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AB - 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.

KW - Combinatorial feature selection

KW - Combinatorics of binary matrices

KW - Dimension reduction

KW - Fixed-parameter tractability

KW - Machine learning

KW - Minimal reduct problem

KW - NP-hardness

KW - W-hardness

KW - Δ-Systems

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JO - Journal of Computer and System Sciences

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Exploiting hidden structure in selecting dimensions that distinguish vectors

Abstract

Keywords

ASJC Scopus subject areas

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