Abstract
Vertex Cover and its variants have always been in the focus of study of Parameterized Algorithmics. This can be also claimed for the emergent area of Parameterized Approximation. While Vertex Cover is known to be solvable in time \(\mathcal{O}^*(c^k)\) with some c < 2, this is not the case for variants like Connected Vertex Cover and others that impose some connectivity requirements on the desired cover. The reason behind is the two-phase approach that is taken for this kind of problems. We show that this barrier can be overcome when we are only interested in approximate solutions. More specifically, we prove that a factor-1.5 approximative solution for Total Vertex Cover can be found in time \(\mathcal{O}^*(1.151^{k})\), where k is some bound on the optimum solution.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Binkele-Raible, D., Fernau, H.: Parameterized measure & conquer for problems with no small kernels. Algorithmica 64, 189–212 (2012)
Bourgeois, N., Escoffier, B., Paschos, V.T.: Approximation of max independent set, min vertex cover and related problems by moderately exponential algorithms. Discrete Applied Mathematics 159(17), 1954–1970 (2011)
Brankovic, L., Fernau, H.: Combining Two Worlds: Parameterised Approximation for Vertex Cover. In: Cheong, O., Chwa, K.-Y., Park, K. (eds.) ISAAC 2010, Part I. LNCS, vol. 6506, pp. 390–402. Springer, Heidelberg (2010)
Brankovic, L., Fernau, H.: Parameterized Approximation Algorithms for Hitting Set. In: Solis-Oba, R., Persiano, G. (eds.) WAOA 2011. LNCS, vol. 7164, pp. 63–76. Springer, Heidelberg (2012)
Chawla, S., Krauthgamer, R., Kumar, R., Rabani, Y., Sivakumar, D.: On the hardness of approximating multicut and sparsest-cut. Computational Complexity 15(2), 94–114 (2006)
Chen, J., Kanj, I.A., Jia, W.: Vertex cover: further observations and further improvements. Journal of Algorithms 41, 280–301 (2001)
Fellows, M.R., Kulik, A., Rosamond, F., Shachnai, H.: Parameterized Approximation via Fidelity Preserving Transformations. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part I. LNCS, vol. 7391, pp. 351–362. Springer, Heidelberg (2012)
Fernau, H., Fomin, F.V., Philip, G., Saurabh, S.: The Curse of Connectivity: t-Total Vertex (Edge) Cover. In: Thai, M.T., Sahni, S. (eds.) COCOON 2010. LNCS, vol. 6196, pp. 34–43. Springer, Heidelberg (2010)
Fernau, H., Manlove, D.F.: Vertex and edge covers with clustering properties: Complexity and algorithms. Journal of Discrete Algorithms 7, 149–167 (2009)
Khot, S.: On the power of unique 2-prover 1-round games. In: Reif, J.F. (ed.) Proceedings on 34th Annual ACM Symposium on Theory of Computing, STOC, pp. 767–775. ACM Press (2002)
Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2 − ε. Journal of Computer and System Sciences 74, 335–349 (2008)
Marx, D., Razgon, I.: Constant ratio fixed-parameter approximation of the edge multicut problem. Information Processing Letters 109(20), 1161–1166 (2009)
Raman, V., Ramanujan, M.S., Saurabh, S.: Paths, Flowers and Vertex Cover. In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 382–393. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fernau, H. (2012). Saving on Phases: Parameterized Approximation for Total Vertex Cover. In: Arumugam, S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2012. Lecture Notes in Computer Science, vol 7643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35926-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-35926-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35925-5
Online ISBN: 978-3-642-35926-2
eBook Packages: Computer ScienceComputer Science (R0)