Abstract
In this paper, we deal with the problem of finding quasi-independent sets in graphs. This problem is formally defined in three versions, which are shown to be polynomially equivalent. The one that looks most general, namely, f-QIS, consists of, given a graph and a non-decreasing function f, finding a maximum size subset Q of the vertices of the graph, such that the number of edges in the induced subgraph is less than or equal to f(|Q|). For this problem, we show an exact solution method that runs within time \(O^*(2^{\frac{d-27/23}{d+1}n})\) on graphs of average degree bounded by d. For the most specifically defined γ-QIS and k-QIS problems, several results on complexity and approximation are shown, and greedy algorithms are proposed, analyzed and tested.
This work is partially supported by the French Agency for Research under the DEFIS program TODO, ANR-09-EMER-010.
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Bourgeois, N., Giannakos, A., Lucarelli, G., Milis, I., Paschos, V.T., Pottié, O. (2010). The max quasi-independent set Problem. In: Ablayev, F., Mayr, E.W. (eds) Computer Science – Theory and Applications. CSR 2010. Lecture Notes in Computer Science, vol 6072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13182-0_6
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DOI: https://doi.org/10.1007/978-3-642-13182-0_6
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