Abstract
We prove a small linear-size kernel for the connected dominating set problem in planar graphs through data reduction. Our set of rules efficiently reduce a planar graph G with n vertices and connected dominating number γ c (G) to a kernel of size at most 413γ c (G) in O(n 3) time answering the question of whether the connectivity criteria hinders the construction of small kernels, negatively (in case of the planar connected dominating set). Our result gives a fixed-parameter algorithm of time \((2^{O(\sqrt{\gamma_c(G)})}\cdot \gamma_c(G) + n^3)\) using the standard branch-decomposition based approach.
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Gu, Q., Imani, N. (2010). Connectivity Is Not a Limit for Kernelization: Planar Connected Dominating Set. In: López-Ortiz, A. (eds) LATIN 2010: Theoretical Informatics. LATIN 2010. Lecture Notes in Computer Science, vol 6034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12200-2_4
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DOI: https://doi.org/10.1007/978-3-642-12200-2_4
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