Abstract
In the Cluster Editing problem, a graph is to be changed to a disjoint union of cliques by at most k operations of edge insertion or edge deletion. Improving on the best previously known quadratic-size polynomial-time kernelization, we describe how a crown-type structural reduction rule can be used to obtain a 6k kernelization bound.
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References
Abu-Khzam, F., Collins, R., Fellows, M., Langston, M., Suters, W.H., Symons, C.: Kernelization algorithms for the vertex cover problem: theory and experiments. In: Proceedings of ALENEX 2004, pp. 62–69. ACM-SIAM Publications (2004)
Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Machine Learning 56, 89–113 (2004) (Preliminary version In: Proceedings 43rd IEEE FOCS 2002, pp. 238–247)
Baldwin, N.E., Chesler, E.J., Kirov, S., Langston, M.A., Snoddy, J.R., Williams, R.W., Zhang, B.: Computational, integrative and comparative methods for the elucidation of gene regulatory networks. J. Biomedicine and Biotechnology 2, 172–180 (2005)
Baldwin, N.E., Collins, R.L., Langston, M.A., Leuze, M.R., Symons, C.T., Voy, B.H.: High performance computational tools for motif discovery. In: Proceedings of the IEEE International Workshop on High Performance Computational Biology (HiCOMB). IEEE Computer Society Press, Los Alamitos (2004)
Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Information Processing Letters 58, 171–176 (1996)
Chlebík, M., Chlebíková, J.: Improvement of Nemhauser-Trotter theorem and its applications in parameterized complexity. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 174–186. Springer, Heidelberg (2004)
Chor, B., Fellows, M., Juedes, D.: Linear kernels in linear time. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 36–53. Springer, Heidelberg (2004)
Charikar, M., Guruswami, V., Wirth, A.: Clustering with qualitative information. Journal of Computer and System Sciences 71, 360–383 (2005)
Chen, Z.Z., Jiang, T., Lin, G.: Computing phylogenetic roots with bounded degrees and errors. SIAM J. Computing 32, 864–879 (2003)
Damaschke, P.: On the fixed-parameter enumerability of cluster editing. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 283–294. Springer, Heidelberg (2005)
Damaschke, P.: Fixed-parameter tractable generalizations of cluster editing. In: Calamoneri, T., Finocchi, I., Italiano, G.F. (eds.) CIAC 2006. LNCS, vol. 3998, pp. 321–332. Springer, Heidelberg (2006)
Damaschke, P.: Parameterized enumeration, transversals, and imperfect phylogeny reconstruction. Theoretical Computer Science 351, 337–350 (2006)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)
Dehne, F., Fellows, M., Rosamond, F., Shaw, P.: Greedy localization, iterative compression and modeled crown reductions: new FPT techniques, an improved algorithm for set splitting and a novel 2k kernelization for vertex cover. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 271–280. Springer, Heidelberg (2004)
Dehne, F., Langston, M.A., Luo, X., Pitre, S., Shaw, P., Zhang, Y.: The Cluster Editing problem: implementations and experiments. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 13–24. Springer, Heidelberg (2006)
Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)
Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39, 321–347 (2004)
Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Graph-modeled data clustering: exact algorithms for clique generation. Theory of Computing Systems 38, 373–392 (2005) (preliminary version In: Proceedings of the 5th Italian Conference on Algorithms and Complexity (CIAC 2003). Lecture Notes in Computer Science 2653, pp. 108–119. Springer-Verlag (2003))
Guo, J.: Manuscript (2007)
Krivanek, M., Moravek, J.: NP-hard problems in hierarchical tree clustering. Acta Informatica 23, 311–323 (1986)
Niedermeier, R.: Invitation to Fixed Parameter Algorithms. Oxford University Press, Oxford (2006)
Nemhauser, G., Trotter, L.: Vertex packings: structural properties and algorithms. Mathematical Programming 8, 232–248 (1975)
Prieto-Rodriguez, E.: Systematic kernelization in FPT algorithm design. Ph.D. Thesis, School of EE&CS, University of Newcastle, Australia (2005)
Prieto, E., Sloper, C.: Looking at the stars. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 138–148. Springer, Heidelberg (2004)
Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. Discrete Applied Mathematics 144, 173–182 (2004) (Preliminary version In: 28th WG 2002, LNCS 2573, pp. 379–390 (2002))
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Fellows, M., Langston, M., Rosamond, F., Shaw, P. (2007). Efficient Parameterized Preprocessing for Cluster Editing . In: Csuhaj-Varjú, E., Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 2007. Lecture Notes in Computer Science, vol 4639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74240-1_27
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DOI: https://doi.org/10.1007/978-3-540-74240-1_27
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