Abstract
We propose a framework for the complexity of algorithms for FPT problems with two separate parameters k,m and with exponential time bounds O *(x k y m) where x,y > 1 are constant bases. An optimal combination of bases x,y can be chosen depending on the ratio m/k. As a first illustration we apply the framework to the problem of finding, in a graph, a vertex cover of size k that leaves at most m edges uncovered. We report the best branching rules we could find so far, for all ranges of ratio m/k.
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References
Balasubramanian, R., Fellows, M.R., Raman, V.: An Improved Fixed-Parameter Algorithm for Vertex Cover. Info. Proc. Letters 65, 163–168 (1998)
Bar-Yehuda, R., Hermelin, D., Rawitz, D.: An Extension of the Nemhauser-Trotter Theorem to Generalized Vertex Cover with Applications. In: WAOA 2009. LNCS, vol. 5893. Springer, Heidelberg (to appear, 2010)
Böcker, S., Briesemeister, S., Bui, Q.B.A., Truß, A.: Going Weighted: Parameterized Algorithms for Cluster Editing. In: Yang, B., Du, D.-Z., Wang, C.A. (eds.) COCOA 2008. LNCS, vol. 5165, pp. 1–12. Springer, Heidelberg (2008)
Chen, J., Kanj, I.A., Xia, G.: A Note on Search Trees. Tecnical Report TR05-006.pdf (2005), facweb.cs.depaul.edu/research/TechReports/
Chen, J., Kanj, I.A., Xia, G.: Simplicity is Beauty: Improved Upper Bounds for Vertex Cover. Technical Report TR05-008.pdf (2005), cdm.depaul.edu/research/Documents/TechnicalReports/2005/
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)
Guo, J., Niedermeier, R., Wernicke, S.: Parameterized Complexity of Generalized Vertex Cover Problems. In: Dehne, F., López-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol. 3608, pp. 36–48. Springer, Heidelberg (2005)
Hüffner, F., Komusiewicz, C., Moser, H., Niedermeier, R.: Fixed-Parameter Algorithms for Cluster Vertex Deletion. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds.) LATIN 2008. LNCS, vol. 4957, pp. 711–722. Springer, Heidelberg (2008)
Kneis, J., Langer, A., Rossmanith, P.: Improved Upper Bounds for Partial Vertex Cover. In: Broersma, H., Erlebach, T., Friedetzky, T., Paulusma, D. (eds.) WG 2008. LNCS, vol. 5344, pp. 240–251. Springer, Heidelberg (2008)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford Lecture Series in Math. and its Appl. Oxford Univ. Press, Oxford (2006)
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Damaschke, P. (2009). Pareto Complexity of Two-Parameter FPT Problems: A Case Study for Partial Vertex Cover. In: Chen, J., Fomin, F.V. (eds) Parameterized and Exact Computation. IWPEC 2009. Lecture Notes in Computer Science, vol 5917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11269-0_9
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DOI: https://doi.org/10.1007/978-3-642-11269-0_9
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