Free Online Productivity Tools
i2Speak
i2Symbol
i2OCR
iTex2Img
iWeb2Print
iWeb2Shot
i2Type
iPdf2Split
iPdf2Merge
i2Bopomofo
i2Arabic
i2Style
i2Image
i2PDF
iLatex2Rtf
Sci2ools

ICALP

2011

Springer

2011

Springer

We study a family of graph clustering problems where each cluster has to satisfy a certain local requirement. Formally, let µ be a function on the subsets of vertices of a graph G. In the (µ, p, q)-PARTITION problem, the task is to ﬁnd a partition of the vertices where each cluster C satisﬁes the requirements that (1) at most q edges leave C and (2) µ(C) ≤ p. Our ﬁrst result shows that if µ is an arbitrary polynomial-time computable monotone function, then (µ, p, q)PARTITION can be solved in time nO(q) , i.e., it is polynomial-time solvable for every ﬁxed q. We study in detail three concrete functions µ (number of nonedges in the cluster, maximum degree of nonedges in the cluster, number of vertices in the cluster), which correspond to natural clustering problems. For these functions, we show that (µ, p, q)-PARTITION can be solved in time 2O(p) · nO(1) and in randomized time 2O(q) · nO(1) , i.e., the problem is ﬁxed-parameter tractable parameterized by p or by q.

Related Content

Added |
29 Aug 2011 |

Updated |
29 Aug 2011 |

Type |
Journal |

Year |
2011 |

Where |
ICALP |

Authors |
Daniel Lokshtanov, Dániel Marx |

Comments (0)