Abstract
We examine the behavior of two kernelization techniques for the vertex cover problem viewed as preprocessing algorithms. Specifically, we deal with the kernelization algorithms of Buss and of Nemhauser & Trotter. Our evaluation is applied to random graphs generated under the preferred attachment model, which is usually met in real word applications such as web graphs and others. Our experiments indicate that, in this model, both kernelization algorithms (and, specially, the Nemhauser & Trotter algorithm) reduce considerably the input size of the problem and can serve as very good preprocessing algorithms for vertex cover, on the preferential attachment graphs.
This research was supported by the EU 6th FP under contract 001907 (DELIS). The first author was partially supported by the Distinció per a la Promoció de la Recerca de la GC, 2002.
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
Abu-Khzam, F.N., Collins, R.L., Fellows, M.R., Langston, M.A., Suters, W.H., Symons, C.T.: Kernelization algorithms for the vertex cover problem: Theory and experiments. In: Sixth Workshop on Algorithm Engineering and Experiments and the First Workshop on Analytic Algorithmics and Combinatorics, New Orleans, LA, USA, pp. 62–69. SIAM, Philadelphia (2004)
Barabási, A.-L.: Emergence of scaling in complex networks. In: Handbook of graphs and networks, pp. 69–84. Wiley-VCH, Weinheim (2003)
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Bollobás, B., Riordan, O., Spencer, J., Tusnády, G.: The degree sequence of a scale-free random graph process. Random Structures Algorithms 18(3), 279–290 (2001)
Buss, J.F., Goldsmith, J.: Nondeterminism within p. SIAM J. Computing 22, 560–572 (1993)
Chen, J., Kanj, I.A., Xia, G.: Simplicity is beauty: Improved upper bounds for vertex cover. Technical Report 05-008, Texas A&M University, Utrecht, the Netherlands (April 2005)
Clauset, A., Moore, C.: Accuracy and scaling phenomena in internet mapping. Phys. Rev. Lett. 94 (2005)
Downey, R.G., Fellows, M.R.: Parameterized complexity. In: Monographs in Computer Science, Springer, New York (1999)
Fellows, M.R.: Parameterized complexity: the main ideas and some research frontiers. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, Springer, Heidelberg (2001)
Fellows, M.R.: Blow-ups, win/win’s, and crown rules: Some new directions in fpt. In: Bodlaender, H.L. (ed.) WG 2003. LNCS, vol. 2880, pp. 1–12. Springer, Heidelberg (2003)
Fomin, F.V., Grandoni, F., Kratsch, D.: Large measure and conquer: A simple O (20.288 n) independent set algorithm. In: 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2006), ACM and SIAM, New York (2006)
Håstad, J.: Some optimal inapproximability results (electronic). J. ACM 48(4), 798–859 (2001)
Karakostas, G.: A better approximation ratio for the vertex cover problem. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1043–1050. Springer, Heidelberg (2005)
Karp, R.M.: Reducibility among combinatorial problems. In: Complexity of computer computations (Proc. Sympos., IBM Thomas J. Watson Res. Center, Yorktown Heights, N.Y., 1972), pp. 85–103. Plenum, New York (1972)
Monien, B., Speckenmeyer, E.: Ramsey numbers and an approximation algorithm for the vertex cover problem. Acta Inform. 22(1), 115–123 (1985)
Nemhauser, G.L., Trotter Jr., L.E.: Vertex packings: structural properties and algorithms. Math. Programming 8, 232–248 (1975)
Newman, M.E.J.: Random graphs as models of networks. In: Handbook of graphs and networks, pp. 35–68. Wiley-VCH, Weinheim (2003)
Robson, J.M.: Finding a maximum independent set in time O(2n/4). manuscript (2001), http://dept-info.labri.fr/~robson/mis/techrep.html
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Díaz, J., Petit, J., Thilikos, D.M. (2006). Kernels for the Vertex Cover Problem on the Preferred Attachment Model. In: Àlvarez, C., Serna, M. (eds) Experimental Algorithms. WEA 2006. Lecture Notes in Computer Science, vol 4007. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11764298_21
Download citation
DOI: https://doi.org/10.1007/11764298_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34597-8
Online ISBN: 978-3-540-34598-5
eBook Packages: Computer ScienceComputer Science (R0)