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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abello, J., Resende, M.G.C., Sudarsky, S.: Massive quasi-clique detection. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 598–612. Springer, Heidelberg (2002)
Asahiro, Y., Iwama, K., Tamaki, H., Tokuyama, T.: Greedily finding a dense subgraph. Journal of Algorithms 34(2), 203–221 (2000)
Boginski, V., Butenko, S., Pardalos, P.: Mining market data: a network approach. Computers and Operations Research (2005), http://www.sciencedirect.com
Bourgeois, N., Giannakos, A., Lucarelli, G., Milis, I., Paschos, V.T., Pottié, O.: The The Max Quasi-Independent Set Problem. Cahier du LAMSADE (292) (2010)
Corneil, D.G., Perl, Y.: Clustering and domination in perfect graphs. Discrete Applied Mathematics 9, 27–39 (1984)
Feige, U., Kortsarz, G., Peleg, D.: The dense k-subgraph problem. Algorithmica 29(3), 410–421 (2001)
Halldórsson, M.M., Radhakrishnan, J.: Greed is good: approximating independent sets in sparse and bounded-degree graphs. In: Proceedings of STOC 1994, pp. 439–448 (1994)
Hartwell, L.H., Hopfield, J.J., Leibler, S., Murray, A.W.: From molecular to modular cell biology. Nature 402, C47–C52 (1999)
Hochbaum, D.S., Goldschmidt, O.: k-edge subgraph problems. Discrete Applied Mathematics 74(2), 159–169 (1997)
Krishnamoorthy, M.S., Deo, N.: Node-deletion NP-complete problems. SIAM J. Comput. 8, 619–625 (1979)
Yannakakis, M., Lewis, J.: The node-deletion problem for hereditary properties is NP-complete. Journal of Computer and System Sciences 20(2), 219–230 (1980)
Zissimopoulos, V.: Private communication
Zuckerman, D.: Linear degree extractors and the inapproximability of max clique and chromatic number. In: Proceedings of STOC 2006, pp. 681–690 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-13182-0_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13181-3
Online ISBN: 978-3-642-13182-0
eBook Packages: Computer ScienceComputer Science (R0)