# Clustering with local restrictions

Lokshtanov, D and Marx, Dániel
(2013)
*Clustering with local restrictions.*
INFORMATION AND COMPUTATION, 222.
pp. 278-292.
ISSN 0890-5401
MTMT:2156222; doi:10.1016/j.ic.2012.10.016

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## Abstract

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 into clusters 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 (the number of vertices in the cluster, number of nonedges in the cluster, maximum number of non-neighbors a vertex has 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 time 2 O(q)×nO(1) on n-vertex graphs, i.e., the problem is fixed-parameter tractable parameterized by p or by q. © 2012 Elsevier Inc. All rights reserved.

Item Type: | ISI Article |
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Uncontrolled Keywords: | Graph theory, Information Systems, Computational methods, Polynomial-time, Partition problem, Parameterized, Natural clustering, N-vertex graph, Monotone functions, Graph clustering |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

SWORD Depositor: | MTMT Injector |

Depositing User: | EPrints Admin |

Date Deposited: | 05 Feb 2014 12:32 |

Last Modified: | 05 Feb 2014 15:46 |

URI: | http://eprints.sztaki.hu/id/eprint/7528 |

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