Abstract
We study the complexity of editing a graph into a target graph with any fixed critical-clique graph. The problem came up in practice, in mining a huge word similarity graph for well structured word clusters. It also adds to the rich field of graph modification problems. We show in a generic way that several variants of this problem are in SUBEPT. As a special case, we give a tight time bound for edge deletion to obtain a single clique and isolated vertices, and we round up this study with NP-completeness results for a number of target graphs.
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
Burzyn, P., Bonomo, F., Durán, G.: NP-completeness Results for Edge Modification Problems. Discr. Appl. Math. 154, 1824–1844 (2006)
Cai, L.: Fixed-Parameter Tractability of Graph Modification Problems for Hereditary Properties. Inf. Proc. Lett. 58, 171–176 (1996)
Chen, J., Kanj, I.A., Xia, G.: Improved Upper Bounds for Vertex Cover. Theor. Comp. Sci. 411, 3736–3756 (2010)
Dickson, L.E.: Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors. Am. J. Math. 35, 413–422 (1913)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, New York (1999)
Fellows, M.R., Guo, J., Komusiewicz, C., Niedermeier, R., Uhlmann, J.: Graph-Based Data Clustering with Overlaps. Discr. Optim. 8, 2–17 (2011)
Fomin, F.V., Kratsch, S., Pilipczuk, M., Pilipczuk, M., Villanger, Y.: Tight Bounds for Parameterized Complexity of Cluster Editing. In: Portier, N., Wilke, T. (eds.) STACS 2013, Dagstuhl. LIPIcs, vol. 20, pp. 32–43 (2013)
Guo, J.: A More Effective Linear Kernelization for Cluster Editing. In: Chen, B., Paterson, M., Zhang, G. (eds.) ESCAPE 2007. LNCS, vol. 4614, pp. 36–47. Springer, Heidelberg (2007)
Guo, J., Niedermeier, R., Wernicke, S.: Parameterized Complexity of Vertex Cover Variants. Theory Comput. Syst. 41, 501–520 (2007)
Natanzon, A., Shamir, R., Sharan, R.: Complexity Classification of some Edge Modification Problems. Discr. Appl. Math. 113, 109–128 (2001)
Peeters, R.: The Maximum Edge Biclique Problem is NP-complete. Discr. Appl. Math. 131, 651–654 (2003)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford Lecture Series in Math. and its Appl. Oxford Univ. Press (2006)
Shamir, R., Sharan, R., Tsur, D.: Cluster Graph Modification Problems. Discr. Appl. Math. 144, 173–182 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Damaschke, P., Mogren, O. (2014). Editing the Simplest Graphs. In: Pal, S.P., Sadakane, K. (eds) Algorithms and Computation. WALCOM 2014. Lecture Notes in Computer Science, vol 8344. Springer, Cham. https://doi.org/10.1007/978-3-319-04657-0_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-04657-0_24
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04656-3
Online ISBN: 978-3-319-04657-0
eBook Packages: Computer ScienceComputer Science (R0)