Abstract
The Maximum Cycle Packing problem is an important class of NP-hard problems, which has lots of applications in many fields. In this paper, we study Parameterized Planar Vertex-Disjoint Cycle Packing problem, which is to find k vertex-disjoint cycles in a given planar graph. The current best kernel size for this problem is \(1209k-1317\). Based on properties of maximal cycle packing, small cycles, degree-2 paths, and new reduction rules given, a kernel of size \(415k-814\) is presented for Parameterized Planar Vertex-Disjoint Cycle Packing problem.
This work is supported by the National Natural Science Foundation of China under Grants (61420106009, 61232001, 61472449, 61672536).
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References
Bodlaender, H.L., Penninkx, E., Tan, R.B.: A linear kernel for the \(k\)-disjoint cycle problem on planar graphs. In: Proceedings of 19th International Symposium on Algorithms and Computation, pp. 306–317 (2008)
Kloks, T., Lee, C.M., Liu, J.: New algorithms for \(k\)-face cover, \(k\)-feedback vertex set, and \(k\)-disjoint cycles on plane and planar graphs. In: Proceedings of 28th International Workshop on Graph-Theoretic Concepts in Computer Science, pp. 282–295 (2002)
Kakimura, N., Kawarabayashi, K., Marx, D.: Packing cycles through prescribed vertices. J. Comb. Theor. Ser. B 101(5), 378–381 (2011)
Grohe, M., Grüber, M.: Parameterized approximability of the disjoint cycle problem. In: Proceedings of 34th International Colloquium on Automata, Languages and Programming, pp. 363–374 (2007)
Bodlaender, H.L., Thomassé, S., Yeo, A.: Kernel bounds for disjoint cycles and disjoint paths. Theor. Comput. Sci. 412(35), 4570–4578 (2011)
Fellows, M., Heggernes, P., Rosamond, F., Sloper, C., Telle, J.A.: Finding \(k\) disjoint triangles in an arbitrary graph. In: Proceedings of 30th International Workshop on Graph-Theoretic Concepts in Computer Science, pp. 235–244 (2004)
Guo, J., Niedermeier, R.: Linear problem kernels for NP-Hard problems on planar graphs. In: Proceedings of 34th International Colloquium on Automata, Languages and Programming, pp. 375–386 (2007)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman & Co., New York (1979)
Agrawal, A., Lokshtanov, D., Majumdar, D., Mouawad, A.E., Saurabh, S.: Kernelization of cycle packing with relaxed disjointness constraints. In: Proceedings of 43rd International Colloquium on Automata, Languages, and Programming, pp. 26:1–26:14 (2016)
Bodlaender, H.L., Jansen, B.M.P., Kratsch, S.: Preprocessing for treewidth: a combinatorial analysis through kernelization. SIAM J. Discret. Math. 27(4), 2108–2142 (2013)
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Feng, Q., Liao, X., Wang, J. (2017). Planar Vertex-Disjoint Cycle Packing: New Structures and Improved Kernel. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10628. Springer, Cham. https://doi.org/10.1007/978-3-319-71147-8_37
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DOI: https://doi.org/10.1007/978-3-319-71147-8_37
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