Line segment covering of cells in arrangements

Matias Korman, Sheung Hung Poon, Marcel Roeloffzen

Research output: Journal PublicationArticlepeer-review

6 Citations (Scopus)


Given a collection L of line segments, we consider its arrangement and study the problem of covering all cells with line segments of L. That is, we want to find a minimum-size set L of line segments such that every cell in the arrangement has a line from L defining its boundary. We show that the problem is NP-hard, even when all segments are axis-aligned. In fact, the problem is still NP-hard when we only need to cover rectangular cells of the arrangement. For the latter problem we also show that it is fixed parameter tractable with respect to the size of the optimal solution. Finally we provide a linear time algorithm for the case where cells of the arrangement are created by recursively subdividing a rectangle using horizontal and vertical cutting segments.

Original languageEnglish
Pages (from-to)25-30
Number of pages6
JournalInformation Processing Letters
Publication statusPublished - Jan 2018
Externally publishedYes


  • Computational geometry
  • FPT
  • Geometric graph
  • NP-hardness
  • Vertex cover

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications


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