Fully-dynamic hierarchical graph clustering using cut trees

Authors:
Christof Doll;Tanja Hartmann;Dorothea Wagner
Affiliations:
Department of Informatics, Karlsruhe Institute of Technology;Department of Informatics, Karlsruhe Institute of Technology;Department of Informatics, Karlsruhe Institute of Technology
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

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Abstract

Algorithms or target functions for graph clustering rarely admit quality guarantees or optimal results in general. However, a hierarchical clustering algorithm by Flake et al., which is based on minimum s-t-cuts whose sink sides are of minimum size, yields such a provable guarantee. We introduce a new degree of freedom to this method by allowing arbitrary minimum s-t-cuts and show that this unrestricted algorithm is complete, i.e., any clustering hierarchy based on minimum s-t-cuts can be found by choosing the right cuts. This allows for a more comprehensive analysis of a graph's structure. Additionally, we present a dynamic version of the unrestricted approach which employs this new degree of freedom to maintain a hierarchy of clusterings fulfilling this quality guarantee and effectively avoid changing the clusterings.