Abstract
We examine the parameterized complexity of t -Dominating Set, the problem of finding a set of at most k nodes that dominate at least t nodes of a graph G = (V,E). The classic NP-complete problem Dominating Set, which can be seen to be t -Dominating Set with the restriction that t = n, has long been known to be W[2]-complete when parameterized in k. Whereas this implies W[2]-hardness for t -Dominating Set and the parameter k, we are able to prove fixed-parameter tractability for t -Dominating Set and the parameter t. More precisely, we obtain a quintic problem kernel and a randomized \(O((4+\varepsilon)^t\textit{poly}(n))\) algorithm. The algorithm is based on the divide-and-color method introduced to the community earlier this year, rather intuitive and can be derandomized using a standard framework.
Supported by the DFG under grant RO 927/7-1.
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Kneis, J., Mölle, D., Rossmanith, P. (2007). Partial vs. Complete Domination: t-Dominating Set. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds) SOFSEM 2007: Theory and Practice of Computer Science. SOFSEM 2007. Lecture Notes in Computer Science, vol 4362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69507-3_31
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DOI: https://doi.org/10.1007/978-3-540-69507-3_31
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