Abstract
The NP-hard Colorful Components problem is a graph partitioning problem on vertex-colored graphs. We identify a new application of Colorful Components in the correction of Wikipedia interlanguage links, and describe and compare three exact and two heuristic approaches. In particular, we devise two ILP formulations, one based on Hitting Set and one based on Clique Partition. Furthermore, we use the recently proposed implicit hitting set framework [Karp, JCSS 2011; Chandrasekaran et al., SODA 2011] to solve Colorful Components. Finally, we study a move-based and a merge-based heuristic for Colorful Components. We can optimally solve Colorful Components for Wikipedia link correction data; while the Clique Partition-based ILP outperforms the other two exact approaches, the implicit hitting set is a simple and competitive alternative. The merge-based heuristic is very accurate and outperforms the move-based one. The above results for Wikipedia data are confirmed by experiments with synthetic instances.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ashley, M.V., Berger-Wolf, T.Y., Chaovalitwongse, W., DasGupta, B., Khokhar, A., Sheikh, S.: An implicit cover problem in wild population study. Discrete Mathematics, Algorithms and Applications 2(1), 21–31 (2010)
Avidor, A., Langberg, M.: The multi-multiway cut problem. Theoretical Computer Science 377(1-3), 35–42 (2007)
Bolikowski, Ł.: Scale-free topology of the interlanguage links in Wikipedia. Technical Report arXiv:0904.0564v2, arXiv (2009)
Bruckner, S., Hüffner, F., Komusiewicz, C., Niedermeier, R., Thiel, S., Uhlmann, J.: Partitioning into colorful components by minimum edge deletions. In: Kärkkäinen, J., Stoye, J. (eds.) CPM 2012. LNCS, vol. 7354, pp. 56–69. Springer, Heidelberg (2012)
Böcker, S., Briesemeister, S., Klau, G.W.: Exact algorithms for cluster editing: Evaluation and experiments. Algorithmica 60(2), 316–334 (2011)
Chandrasekaran, K., Karp, R.M., Moreno-Centeno, E., Vempala, S.: Algorithms for implicit hitting set problems. In: Proc. 22nd SODA, pp. 614–629. SIAM (2011)
Chopra, S., Rao, M.R.: On the multiway cut polyhedron. Networks 21(1), 51–89 (1991)
Corel, E., Pitschi, F., Morgenstern, B.: A min-cut algorithm for the consistency problem in multiple sequence alignment. Bioinformatics 26(8), 1015–1021 (2010)
Grötschel, M., Wakabayashi, Y.: A cutting plane algorithm for a clustering problem. Mathematical Programming 45(1-3), 59–96 (1989)
Görke, R., Schumm, A., Wagner, D.: Experiments on density-constrained graph clustering. In: Proc. 2012 ALENEX, pp. 1–15. SIAM (2012)
Karp, R.M.: Heuristic algorithms in computational molecular biology. Journal of Computer and System Sciences 77(1), 122–128 (2011)
Lee, T., Wang, Z., Wang, H., Hwang, S.: Web scale taxonomy cleansing. In: Proceedings of the VLDB Endowment, vol. 4, pp. 1295–1306 (2011)
de Melo, G., Weikum, G.: Untangling the cross-lingual link structure of Wikipedia. In: Proc. 48th ACL, pp. 844–853. ACM (2010)
de Melo, G., Weikum, G.: MENTA: inducing multilingual taxonomies from Wikipedia. In: Proc. 19th CIKM, pp. 1099–1108. ACM (2010)
Moreno-Centeno, E., Karp, R.M.: The implicit hitting set approach to solve combinatorial optimization problems with an application to multigenome alignment. Operations Research (to appear, 2013)
Oosten, M., Rutten, J.H.G.C., Spieksma, F.C.R.: The clique partitioning problem: Facets and patching facets. Networks 38(4), 209–226 (2001)
Régnier, S.: Sur quelques aspects mathématiques des problèmes de classification automatique. I.C.C. Bulletin 4, 175–191 (1965)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bruckner, S., Hüffner, F., Komusiewicz, C., Niedermeier, R. (2013). Evaluation of ILP-Based Approaches for Partitioning into Colorful Components. In: Bonifaci, V., Demetrescu, C., Marchetti-Spaccamela, A. (eds) Experimental Algorithms. SEA 2013. Lecture Notes in Computer Science, vol 7933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38527-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-38527-8_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38526-1
Online ISBN: 978-3-642-38527-8
eBook Packages: Computer ScienceComputer Science (R0)