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Base Location Problems for Base-Monotone Regions

  • Jinhee Chun
  • Takashi Horiyama
  • Takehiro Ito
  • Natsuda Kaothanthong
  • Hirotaka Ono
  • Yota Otachi
  • Takeshi Tokuyama
  • Ryuhei Uehara
  • Takeaki Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7748)

Abstract

The problem of decomposing a pixel grid into base-monotone regions was first studied in the context of image segmentation. It is known that for a given pixel grid and baselines, one can compute in polynomial time a maximum-weight region that can be decomposed into disjoint base-monotone regions [Chun et al. ISAAC 2009]. We continue this line of research and show the NP-hardness of the problem of optimally locating k baselines in a given n ×n pixel grid. We also present an O(n 3)-time 2-approximation algorithm for this problem. We then study two related problems, the k base-segment problem and the quad-decomposition problem, and present some complexity results for them.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jinhee Chun
    • 1
  • Takashi Horiyama
    • 2
  • Takehiro Ito
    • 1
  • Natsuda Kaothanthong
    • 1
  • Hirotaka Ono
    • 3
  • Yota Otachi
    • 4
  • Takeshi Tokuyama
    • 1
  • Ryuhei Uehara
    • 4
  • Takeaki Uno
    • 5
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Graduate School of Science and EngineeringSaitama UniversitySaitamaJapan
  3. 3.Department of Economic EngineeringKyushu UniversityHigashi-kuJapan
  4. 4.School of Information ScienceJapan Advanced Institute of Science and TechnologyNomiJapan
  5. 5.National Institute of InformaticsChiyoda-kuJapan

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