Abstract
The Cluster Editing problem asks to transform a graph by at most k edge modifications into a disjoint union of cliques. The problem is NP-complete, but several parameterized algorithms are known. We present a novel search tree algorithm for the problem, which improves running time from O*(1.76k) to O*(1.62k). In detail, we can show that we can always branch with branching vector (2,1) or better, resulting in the golden ratio as the base of the search tree size. Our algorithm uses a well-known transformation to the integer-weighted counterpart of the problem. To achieve our result, we combine three techniques: First, we show that zero-edges in the graph enforce structural features that allow us to branch more efficiently. Second, by repeatedly branching we can isolate vertices, releasing costs. Finally, we use a known characterization of graphs with few conflicts.
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References
Böcker, S., Briesemeister, S., Bui, Q.B.A., Truss, A.: Going weighted: Parameterized algorithms for cluster editing. Theor. Comput. Sci. 410(52), 5467–5480 (2009)
Böcker, S., Briesemeister, S., Klau, G.W.: Exact algorithms for cluster editing: Evaluation and experiments. Algorithmica 60(2), 316–334 (2011)
Böcker, S., Damaschke, P.: Even faster parameterized cluster deletion and cluster editing. Inform. Process. Lett. 111(14), 717–721 (2011)
Cao, Y., Chen, J.: Cluster Editing: Kernelization Based on Edge Cuts. In: Raman, V., Saurabh, S. (eds.) IPEC 2010. LNCS, vol. 6478, pp. 60–71. Springer, Heidelberg (2010)
Chen, J., Meng, J.: A 2k Kernel for the Cluster Editing Problem. In: Thai, M.T., Sahni, S. (eds.) COCOON 2010. LNCS, vol. 6196, pp. 459–468. Springer, Heidelberg (2010)
Damaschke, P.: Bounded-Degree Techniques Accelerate Some Parameterized Graph Algorithms. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 98–109. Springer, Heidelberg (2009)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)
Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum-flow problem. J. ACM 35(4), 921–940 (1988)
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)
Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Graph-modeled data clustering: Fixed-parameter algorithms for clique generation. Theor. Comput. Syst. 38(4), 373–392 (2005)
Guo, J.: A more effective linear kernelization for cluster editing. Theor. Comput. Sci. 410(8-10), 718–726 (2009)
Hsu, W.-L., Ma, T.-H.: Substitution Decomposition on Chordal Graphs and Applications. In: Hsu, W.-L., Lee, R.C.T. (eds.) ISA 1991. LNCS, vol. 557, pp. 52–60. Springer, Heidelberg (1991)
Křivánek, M., Morávek, J.: NP-hard problems in hierarchical-tree clustering. Acta. Inform. 23(3), 311–323 (1986)
Marx, D., Razgon, I.: Fixed-parameter tractability of multicut parameterized by the size of the cutset. In: Proc. of ACM Symposium on Theory of Computing, STOC 2011, pp. 469–478. ACM (2011), doi:10.1145/1993636.1993699
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)
Niedermeier, R., Rossmanith, P.: A general method to speed up fixed-parameter-tractable algorithms. Inform. Process. Lett. 73, 125–129 (2000)
Rosamond, F. (ed.): FPT News: The Parameterized Complexity Newsletter (Since 2005), http://fpt.wikidot.com/
Wittkop, T., Emig, D., Lange, S., Rahmann, S., Albrecht, M., Morris, J.H., Böcker, S., Stoye, J., Baumbach, J.: Partitioning biological data with transitivity clustering. Nat. Methods 7(6), 419–420 (2010)
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Böcker, S. (2011). A Golden Ratio Parameterized Algorithm for Cluster Editing. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2011. Lecture Notes in Computer Science, vol 7056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25011-8_7
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DOI: https://doi.org/10.1007/978-3-642-25011-8_7
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