Base-object location problems for base-monotone regions

Jinhee Chun, Takashi Horiyama, Takehiro Ito, Natsuda Kaothanthong, Hirotaka Ono, Yota Otachi, Takeshi Tokuyama, Ryuhei Uehara, Takeaki Uno

Research output: Contribution to journalArticle


A base-monotone region with a base is a subset of the cells in a pixel grid such that if a cell is contained in the region then so are the ones on a shortest path from the cell to the base. The problem of decomposing a pixel grid into disjoint base-monotone regions was first studied in the context of image segmentation. It is known that for a given pixel grid and base-lines, one can compute in polynomial time a maximum-weight region that can be decomposed into disjoint base-monotone regions with respect to the given base-lines (Chun et al., 2012 [4]). We continue this line of research and show the NP-hardness of the problem of optimally locating k base-lines in a given n×n pixel grid. We then present an O(n3)-time 2-approximation algorithm for this problem. We also study two related problems, the k base-segment problem and the quad-decomposition problem, and present some complexity results for them.

Original languageEnglish
Pages (from-to)71-84
Number of pages14
JournalTheoretical Computer Science
Issue numberC
Publication statusPublished - 2014

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Chun, J., Horiyama, T., Ito, T., Kaothanthong, N., Ono, H., Otachi, Y., Tokuyama, T., Uehara, R., & Uno, T. (2014). Base-object location problems for base-monotone regions. Theoretical Computer Science, 555(C), 71-84.