Abstract
In the Cluster Vertex Deletion problem the input is a graph G and an integer k. The goal is to decide whether there is a set of vertices S of size at most k such that the deletion of the vertices of S from G results in a graph in which every connected component is a clique. We give an algorithm for Cluster Vertex Deletion whose running time is O∗(1.811k).
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Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Mach. Learn. 56(1–3), 89–113 (2004)
Ben-Dor, A., Shamir, R., Yakhini, Z.: Clustering gene expression patterns. J. Comput. Biol. 6(3–4), 281–297 (1999)
Boral, A., Cygan, M., Kociumaka, T., Pilipczuk, M.: A fast branching algorithm for cluster vertex deletion. Theory Comput. Syst. 58(2), 357–376 (2016)
Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Inf. Process. Lett. 58(4), 171–176 (1996)
Chang, M. -S., Chen, L. -H., Hung, L. -J., Rossmanith, P., Su, P. -C.: Fixed-parameter algorithms for vertex cover P3. Discrete Optim. 19, 12–22 (2016)
Cygan, M., Fomin, F. V., Kowalik, Ł., Lokshtanov, D., Marx, D., Pilipczuk, M., Saurabh, S.: Parameterized Algorithms. Springer, Berlin (2015)
Fernau, H.: A top-down approach to search-trees: improved algorithmics for 3-hitting set. Algorithmica 57(1), 97–118 (2010)
Fomin, F. V., Gaspers, S., Kratsch, D., Liedloff, M., Saurabh, S.: Iterative compression and exact algorithms. Theor. Comput. Sci. 411 (7–9), 1045–1053 (2010)
Fomin, F. V., Gaspers, S., Lokshtanov, D., Saurabh, S.: Exact algorithms via monotone local search. In: Proceedings of the 27th Symposium on Discrete Algorithms (SODA), pp 764–775 (2016)
Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39(4), 321–347 (2004)
Hüffner, F., Komusiewicz, C., Moser, H., Niedermeier, R.: Fixed-parameter algorithms for cluster vertex deletion. Theory Comput. Syst. 47(1), 196–217 (2010)
Katrenič, J.: A faster FPT algorithm for 3-path vertex cover. Inf. Process. Lett. 116(4), 273–278 (2016)
Tsur, D.: Parameterized algorithm for 3-path vertex cover. Theor. Comput. Sci. 783, 1–8 (2019)
Tu, J.: A fixed-parameter algorithm for the vertex cover P3 problem. Inf. Process. Lett. 115(2), 96–99 (2015)
Wahlström, M.: Algorithms, measures and upper bounds for satisfiability and related problems. PhD thesis, Department of Computer and Information Science, Linköpings Universitet (2007)
Wu, B. Y.: A measure and conquer approach for the parameterized bounded degree-one vertex deletion. In: Proceedings of the 21st International Computing and Combinatorics Conference (COCOON), pp 469–480 (2015)
Xiao, M., Kou, S.: Kernelization and parameterized algorithms for 3-path vertex cover. In: Proceedings of the 14th International Conference on Theory and Applications of Models of Computation (TAMC), pp 654–668 (2017)
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Tsur, D. Faster Parameterized Algorithm for Cluster Vertex Deletion. Theory Comput Syst 65, 323–343 (2021). https://doi.org/10.1007/s00224-020-10005-w
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DOI: https://doi.org/10.1007/s00224-020-10005-w