### Abstract

Graph clustering is an important problem with applications to bioinformatics, community discovery in social networks, distributed computing, etc. While most of the research in this area has focused on clustering using disjoint clusters, many real datasets have inherently overlapping clusters. We compare overlapping and non-overlapping clusterings in graphs in the context of minimizing their conductance. It is known that allowing clusters to overlap gives better results in practice. We prove that overlapping clustering may be significantly better than non-overlapping clustering with respect to conductance, even in a theoretical setting. For minimizing the maximum conductance over the clusters, we give examples demonstrating that allowing overlaps can yield significantly better clusterings, namely, one that has much smaller optimum. In addition for the min-max variant, the overlapping version admits a simple approximation algorithm, while our algorithm for the non-overlapping version is complex and yields worse approximation ratio due to the presence of the additional constraint. Somewhat surprisingly, for the problem of minimizing the sum of conductances, we found out that allowing overlap does not really help. We show how to apply a general technique to transform any overlapping clustering into a non-overlapping one with only a modest increase in the sum of conductances. This uncrossing technique is of independent interest and may find further applications in the future.

Original language | English (US) |
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Title of host publication | LATIN 2012 |

Subtitle of host publication | Theoretical Informatics - 10th Latin American Symposium, Proceedings |

Publisher | Springer Verlag |

Pages | 494-505 |

Number of pages | 12 |

ISBN (Print) | 9783642293436 |

DOIs | |

State | Published - Jan 1 2012 |

Event | 10th Latin American Symposiumon Theoretical Informatics, LATIN 2012 - Arequipa, Peru Duration: Apr 16 2012 → Apr 20 2012 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7256 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 10th Latin American Symposiumon Theoretical Informatics, LATIN 2012 |
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Country | Peru |

City | Arequipa |

Period | 4/16/12 → 4/20/12 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Keywords

- dynamic programming
- graph clustering
- overlapping clustering
- tree decomposition

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## Cite this

*LATIN 2012: Theoretical Informatics - 10th Latin American Symposium, Proceedings*(pp. 494-505). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7256 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-29344-3_42