Abstract
Preprocessing (data reduction or kernelization) as a strategy of coping with hard problems is universally used in almost every implementation. The history of preprocessing, like applying reduction rules simplifying truth functions, can be traced back to the 1950’s [6]. A natural question in this regard is how to measure the quality of preprocessing rules proposed for a specific problem. For a long time the mathematical analysis of polynomial time preprocessing algorithms was neglected. The basic reason for this anomaly was that if we start with an instance I of an NP-hard problem and can show that in polynomial time we can replace this with an equivalent instance I′ with |I′| < |I| then that would imply P=NP in classical complexity.
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
References
Alber, J., Fellows, M.R., Niedermeier, R.: Polynomial-time data reduction for dominating set. J. ACM 51, 363–384 (2004)
Bodlaender, H., Fomin, F.V., Lokshtanov, D., Penninkx, E., Saurabh, S., Thilikos, D.M.: (meta) Kernelization. In: Proceedings of the 50th Annual Symposium on Foundations of Computer Science (FOCS 2009), pp. 629–638. IEEE, Los Alamitos (2009)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1998)
Fomin, F.V., Lokshtanov, D., Saurabh, S., Thilikos, D.M.: Bidimensionality and kernels. In: Proceedings of the 21th ACM-SIAM Symposium on Discrete Algorithms (SODA 2010), pp. 503–510 (2010)
Nemhauser, G.L., Trotter, L.E.: Vertex packings: Structural properties and algorithms. Math. Program. 8, 232–248 (1975)
Quine, W.V.: The problem of simplifying truth functions. Amer. Math. Monthly 59, 521–531 (1952)
Thomassé, S.: A quadratic kernel for feedback vertex set. In: Proceedings of the 20th ACM-SIAM Symposium on Discrete Algorithms (SODA 2009), pp. 115–119 (2009)
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
Fomin, F.V. (2010). Kernelization. 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_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-13182-0_10
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)