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-max quasi-independent set, 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-max quasi-independent set and k-max quasi-independent set problems, several results on complexity and approximation are shown, and greedy algorithms are proposed, analyzed and tested.
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This work is partially supported by the French Agency for Research under the DEFIS program TODO, ANR-09-EMER-010. An extended abstract of this paper has been included in the proceedings of the CSR’10 conference, LNCS 6072.
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Bourgeois, N., Giannakos, A., Lucarelli, G. et al. The max quasi-independent set problem. J Comb Optim 23, 94–117 (2012). https://doi.org/10.1007/s10878-010-9343-5
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DOI: https://doi.org/10.1007/s10878-010-9343-5