### Abstract

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

Title of host publication | Approximation and Online Algorithms |

Publisher | Springer |

Pages | 27-39 |

Volume | 10138 |

Edition | Lecture Notes in Computer Science |

ISBN (Electronic) | 978-3-319-51741-4 |

ISBN (Print) | 978-3-319-51740-7 |

DOIs | |

Publication status | Published - 7 Jan 2017 |

### Publication series

Series | Lecture Notes in Computer Science |
---|---|

Volume | 10138 |

### Keywords

- Graph approximation
- Correlation clustering
- Cluster editing
- PTAS
- k-planarity
- Microscopy cell segmentation

### Cite this

*Approximation and Online Algorithms*(Lecture Notes in Computer Science ed., Vol. 10138, pp. 27-39). Springer. Lecture Notes in Computer Science, Vol.. 10138 https://doi.org/10.1007/978-3-319-51741-4_3

}

*Approximation and Online Algorithms.*Lecture Notes in Computer Science edn, vol. 10138, Springer, Lecture Notes in Computer Science, vol. 10138, pp. 27-39. https://doi.org/10.1007/978-3-319-51741-4_3

**A PTAS for the Cluster Editing Problem on Planar Graphs.** / Berger, Andre; Grigoriev, Alexander; Winokurow, Andrej.

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

TY - CHAP

T1 - A PTAS for the Cluster Editing Problem on Planar Graphs

AU - Berger, Andre

AU - Grigoriev, Alexander

AU - Winokurow, Andrej

N1 - NO DATA USED

PY - 2017/1/7

Y1 - 2017/1/7

N2 - The goal of the cluster editing problem is to add or delete a minimum number of edges from a given graph, so that the resulting graph becomes a union of disjoint cliques. The cluster editing problem is closely related to correlation clustering and has applications, e.g. In image segmentation. For general graphs this problem is apx apx{\mathbb {apx}}-hard. In this paper we present an efficient polynomial time approximation scheme for the cluster editing problem on graphs embeddable in the plane with a few edge crossings. The running time of the algorithm is 2 o(? -1 log(? -1 )) n 2o(?-1log?(?-1))n{2^{o\left( \epsilon ^{-1} \log (\epsilon ^{-1})\right) }n} for planar graphs and 2 o(k 2 ? -1 log(k 2 ? -1 )) n 2o(k2?-1log?(k2?-1))n2^{o\left( k^2\epsilon ^{-1}\log \left( k^2\epsilon ^{-1}\right) \right) }n for planar graphs with at most k crossings.

AB - The goal of the cluster editing problem is to add or delete a minimum number of edges from a given graph, so that the resulting graph becomes a union of disjoint cliques. The cluster editing problem is closely related to correlation clustering and has applications, e.g. In image segmentation. For general graphs this problem is apx apx{\mathbb {apx}}-hard. In this paper we present an efficient polynomial time approximation scheme for the cluster editing problem on graphs embeddable in the plane with a few edge crossings. The running time of the algorithm is 2 o(? -1 log(? -1 )) n 2o(?-1log?(?-1))n{2^{o\left( \epsilon ^{-1} \log (\epsilon ^{-1})\right) }n} for planar graphs and 2 o(k 2 ? -1 log(k 2 ? -1 )) n 2o(k2?-1log?(k2?-1))n2^{o\left( k^2\epsilon ^{-1}\log \left( k^2\epsilon ^{-1}\right) \right) }n for planar graphs with at most k crossings.

KW - Graph approximation

KW - Correlation clustering

KW - Cluster editing

KW - PTAS

KW - k-planarity

KW - Microscopy cell segmentation

U2 - 10.1007/978-3-319-51741-4_3

DO - 10.1007/978-3-319-51741-4_3

M3 - Chapter

SN - 978-3-319-51740-7

VL - 10138

T3 - Lecture Notes in Computer Science

SP - 27

EP - 39

BT - Approximation and Online Algorithms

PB - Springer

ER -