LATIN 2012: Theoretical Informatics
Volume 7256 of the series Lecture Notes in Computer Science pp 494-505
Advantage of Overlapping Clusters for Minimizing Conductance
- Rohit KhandekarAffiliated withIBM T.J. Watson Research Center
- , Guy KortsarzAffiliated withRutgers University
- , Vahab MirrokniAffiliated withGoogle Research
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.
Keywords
graph clustering overlapping clustering tree decomposition dynamic programming- Title
- Advantage of Overlapping Clusters for Minimizing Conductance
- Book Title
- LATIN 2012: Theoretical Informatics
- Book Subtitle
- 10th Latin American Symposium, Arequipa, Peru, April 16-20, 2012. Proceedings
- Pages
- pp 494-505
- Copyright
- 2012
- DOI
- 10.1007/978-3-642-29344-3_42
- Print ISBN
- 978-3-642-29343-6
- Online ISBN
- 978-3-642-29344-3
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- 7256
- Series ISSN
- 0302-9743
- Publisher
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Topics
- Keywords
-
- graph clustering
- overlapping clustering
- tree decomposition
- dynamic programming
- Industry Sectors
- eBook Packages
- Editors
-
- David Fernández-Baca (16)
- Editor Affiliations
-
- 16. Department of Computer Science, Iowa State University
- Authors
-
- Rohit Khandekar (17)
- Guy Kortsarz (18)
- Vahab Mirrokni (19)
- Author Affiliations
-
- 17. IBM T.J. Watson Research Center, USA
- 18. Rutgers University, Camden, USA
- 19. Google Research, New York, USA
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