?. V. Which, Line 3 runs in O * ? /2 ), since |V 2 ? V C| = ? /2 and V \ V C is an independent set. Finally, as B is a bipartite graph, Line 1, a minimum vertex cover can be computed as in [13]. As |V 1 Line 4, use Generic Line 5 runs in O * (2 min{|V 1 |,|V 2 } ) = O * (2 |V 1 | ) = O *

]. S. Arnborg, D. G. Corneil, and A. Proskurowski, -Tree, SIAM Journal on Algebraic Discrete Methods, vol.8, issue.2, pp.277-284, 1987.
DOI : 10.1137/0608024

Y. Asahiro, R. Hassin, and K. Iwama, Complexity of finding dense subgraphs, Discrete Applied Mathematics, vol.121, issue.1-3, pp.15-26, 2002.
DOI : 10.1016/S0166-218X(01)00243-8

A. Bhaskara, M. Charikar, E. Chlamtac, U. Feige, and A. Vijayaraghavan, Detecting high log-densities, Proceedings of the 42nd ACM symposium on Theory of computing, STOC '10, pp.201-210, 2010.
DOI : 10.1145/1806689.1806719

A. Billionnet and F. Roupin, A deterministic approximation algorithm for the densest ksubgraph problem, International Journal of Operational Research, vol.3, pp.301-314, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00596169

A. Björklund, T. Husfeldt, and M. Koivisto, Set Partitioning via Inclusion-Exclusion, SIAM Journal on Computing, vol.39, issue.2, pp.546-563, 2009.
DOI : 10.1137/070683933

H. L. Bodlaender, A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth, SIAM Journal on Computing, vol.25, issue.6, pp.1305-1317, 1996.
DOI : 10.1137/S0097539793251219

N. Bourgeois, B. Escoffier, V. Th, and . Paschos, Approximation of max independent set, min vertex cover and related problems by moderately exponential algorithms, Discrete Applied Mathematics, vol.159, issue.17, pp.1954-1970, 2011.
DOI : 10.1016/j.dam.2011.07.009

N. Bourgeois, B. Escoffier, V. Th, J. M. Paschos, and . Van-rooij, Fast Algorithms for max independent set, Algorithmica, vol.7, issue.3, pp.382-415, 2012.
DOI : 10.1007/s00453-010-9460-7
URL : https://hal.archives-ouvertes.fr/hal-00880187

N. Bourgeois, A. Giannakos, G. Lucarelli, I. Milis, V. Th et al., The max quasi-independent set problem, Journal of Combinatorial Optimization, vol.20, issue.2, pp.94-117, 2012.
DOI : 10.1007/s10878-010-9343-5
URL : https://hal.archives-ouvertes.fr/hal-01185274

L. Brankovic and H. Fernau, Combining Two Worlds: Parameterised Approximation for Vertex Cover, ISAAC'10, pp.390-402, 2010.
DOI : 10.1007/978-3-642-17517-6_35

L. Cai, Parameterized Complexity of Cardinality Constrained Optimization Problems, The Computer Journal, vol.51, issue.1, pp.102-121, 2007.
DOI : 10.1093/comjnl/bxm086

L. Cai and X. Huang, Fixed-parameter approximation: conceptual framework and approximability results, IWPEC'06, pp.96-108, 2006.
DOI : 10.1007/11847250_9
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.2987

J. Chen, I. A. Kanj, and G. Xia, Improved upper bounds for vertex cover, Theoretical Computer Science, vol.411, issue.40-42, pp.3736-3756, 2010.
DOI : 10.1016/j.tcs.2010.06.026
URL : http://doi.org/10.1016/j.tcs.2010.06.026

M. Cygan, L. Kowalik, and M. Wykurz, Exponential-time approximation of weighted set cover, Information Processing Letters, vol.109, issue.16, pp.957-961, 2009.
DOI : 10.1016/j.ipl.2009.05.003

M. Cygan and M. Pilipczuk, Exact and approximate bandwidth, Theoretical Computer Science, vol.411, pp.40-423701, 2010.
DOI : 10.1016/j.tcs.2010.06.018
URL : http://doi.org/10.1016/j.tcs.2010.06.018

R. G. Downey and M. R. Fellows, Parameterized complexity. Monographs in Computer Science, 1999.
DOI : 10.1007/978-1-4612-0515-9
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.3797

R. G. Downey, M. R. Fellows, and C. Mccartin, Parameterized Approximation Problems, IWPEC'06, pp.121-129, 2006.
DOI : 10.1007/11847250_11
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.467.9346

U. Feige, G. Kortsarz, and D. Peleg, The Dense k -Subgraph Problem, Algorithmica, vol.29, issue.3, pp.410-421, 2001.
DOI : 10.1007/s004530010050

F. V. Fomin, F. Grandoni, and D. Kratsch, A measure & conquer approach for the analysis of exact algorithms, Journal of the ACM, vol.56, issue.5, 2009.
DOI : 10.1145/1552285.1552286

F. V. Fomin and K. Høie, Pathwidth of cubic graphs and exact algorithms, Information Processing Letters, vol.97, issue.5, pp.191-196, 2006.
DOI : 10.1016/j.ipl.2005.10.012

M. Fürer, S. Gaspers, and S. P. Kasiviswanathan, An exponential time 2-approximation algorithm for bandwidth, IWPEC'09, pp.173-184, 2009.

M. R. Garey and D. S. Johnson, Computers and intractability: A guide to the theory of NP-completeness, 1979.

S. Khot, Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique, 45th Annual IEEE Symposium on Foundations of Computer Science, pp.136-145, 2004.
DOI : 10.1109/FOCS.2004.59

D. Marx, Parameterized Complexity and Approximation Algorithms, The Computer Journal, vol.51, issue.1, pp.60-78, 2008.
DOI : 10.1093/comjnl/bxm048
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.102.728

H. Moser, Exact algorithms for generalizations of vertex cover, 2005.

D. J. Rader-jr and G. J. Woeginger, The quadratic 0???1 knapsack problem with series???parallel support, Operations Research Letters, vol.30, issue.3, pp.159-166, 2002.
DOI : 10.1016/S0167-6377(02)00122-0

B. Reed, Paths, Stars and the Number Three, Combinatorics, Probability and Computing, vol.17, issue.03, pp.277-295, 1996.
DOI : 10.1002/net.3230070305

J. M. Van-rooij, J. Nederlof, and T. C. Van-dijk, Inclusion/Exclusion Meets Measure and Conquer, ESA'09, pp.554-565, 2009.
DOI : 10.1007/978-3-642-04128-0_50