### 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.

Original language | English |
---|---|

Title of host publication | WALCOM |

Subtitle of host publication | Algorithms and Computation - 7th International Workshop, WALCOM 2013, Proceedings |

Pages | 53-64 |

Number of pages | 12 |

DOIs | |

Publication status | Published - Feb 4 2013 |

Event | 7th International Workshop on Algorithms and Computation, WALCOM 2013 - Kharagpur, India Duration: Feb 14 2013 → Feb 16 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 7748 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 7th International Workshop on Algorithms and Computation, WALCOM 2013 |
---|---|

Country | India |

City | Kharagpur |

Period | 2/14/13 → 2/16/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*WALCOM: Algorithms and Computation - 7th International Workshop, WALCOM 2013, Proceedings*(pp. 53-64). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7748 LNCS). https://doi.org/10.1007/978-3-642-36065-7_7

**Base location problems for base-monotone regions.** / Chun, Jinhee; Horiyama, Takashi; Ito, Takehiro; Kaothanthong, Natsuda; Ono, Hirotaka; Otachi, Yota; Tokuyama, Takeshi; Uehara, Ryuhei; Uno, Takeaki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*WALCOM: Algorithms and Computation - 7th International Workshop, WALCOM 2013, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7748 LNCS, pp. 53-64, 7th International Workshop on Algorithms and Computation, WALCOM 2013, Kharagpur, India, 2/14/13. https://doi.org/10.1007/978-3-642-36065-7_7

}

TY - GEN

T1 - Base location problems for base-monotone regions

AU - Chun, Jinhee

AU - Horiyama, Takashi

AU - Ito, Takehiro

AU - Kaothanthong, Natsuda

AU - Ono, Hirotaka

AU - Otachi, Yota

AU - Tokuyama, Takeshi

AU - Uehara, Ryuhei

AU - Uno, Takeaki

PY - 2013/2/4

Y1 - 2013/2/4

N2 - 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(n3)-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.

AB - 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(n3)-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.

UR - http://www.scopus.com/inward/record.url?scp=84873812867&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873812867&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-36065-7_7

DO - 10.1007/978-3-642-36065-7_7

M3 - Conference contribution

AN - SCOPUS:84873812867

SN - 9783642360640

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 53

EP - 64

BT - WALCOM

ER -