Exploiting hidden structure in selecting dimensions that distinguish vectors

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

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)521-535
Number of pages15
JournalJournal of Computer and System Sciences
Volume82
Issue number3
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

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

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