Abstract
Dealing with the NP-complete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set on planar graphs has a so-called problem kernel of linear size, achieved by two simple and easy to implement reduction rules. This answers an open question from previous work on the parameterized complexity of Dominating Set on planar graphs.
Work supported by the Deutsche Forschungsgemeinschaft (DFG), research project PEAL (Parameterized complexity and Exact ALgorithms), NI 369/1-1,1-2.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Alber, H. L. Bodlaender, H. Fernau, and R. Niedermeier. Fixed parameter algorithms for planar dominating set and related problems. In Proc. 7th SWAT 2000, Springer-Verlag LNCS 1851, pp. 97–110, 2000.
J. Alber, H. Fan, M. R. Fellows, H. Fernau, R. Niedermeier, F. Rosamond, and U. Stege. Refined search tree technique for dominating set on planar graphs. In Proc. 26th MFCS 2001, Springer-Verlag LNCS 2136, pp. 111–122, 2001.
J. Alber, H. Fernau, and R. Niedermeier. Parameterized complexity: exponential speed-up for planar graph problems. In Proc. 28th ICALP 2001, Springer-Verlag LNCS 2076, pp. 261–272, 2001.
J. Alber, H. Fernau, and R. Niedermeier. Graph separators: a parameterized view. In Proc. 7th COCOON 2001, Springer-Verlag LNCS 2108, pp. 318–327, 2001.
J. Alber, J. Gramm, and R. Niedermeier. Faster exact solutions for hard problems: a parameterized point of view. Discrete Mathematics, 229: 3–27, 2001.
J. Alber and R. Niedermeier. Improved tree decomposition based algorithms for domination-like problems. In Proc. 5th LATIN 2002, Springer-Verlag LNCS 2286, pp. 613–627, 2002.
R. Bar-Yehuda and S. Even. A local-ratio theorem for approximating the weighted vertex cover problem. Annals of Discrete Mathematics, 25: 27–46, 1985.
J. Chen, I. A. Kanj, and W. Jia. Vertex cover: further observations and further improvements. Journal of Algorithms, 41:280–301, 2001.
R. G. Downey and M. R. Fellows. Parameterized computational feasibility. In P. Clote, J. Remmel (eds.): Feasible Mathematics II, pp. 219–244. Birkhäuser, 1995.
R. G. Downey and M. R. Fellows. Parameterized Complexity. Monographs in Computer Science. Springer-Verlag, 1999.
M. R. Fellows. Parameterized complexity: the main ideas and some research frontiers. In Proc. 12th ISAAC 2001, Springer-Verlag LNCS 2223, pp. 291–307, 2001.
T. W. Haynes, S. T. Hedetniemi, and P. J. Slater. Fundamentals of Domination in Graphs. Monographs and textbooks in pure and applied Mathematics Vol. 208, Marcel Dekker, 1998.
G. L. Nemhauser and L. E. Trotter. Vertex packing: structural properties and algorithms. Mathematical Programming, 8:232–248, 1975.
F. S. Roberts. Graph Theory and Its Applications to Problems of Society. SIAM Press 1978. Third printing 1993 by Odyssey Press.
J. A. Telle. Complexity of domination-type problems in graphs. Nordic J. Comput. 1:157–171, 1994.
K. Weihe. Covering trains by stations or the power of data reduction. In Proc. 1st ALEX’98, pp. 1–8, 1998.
K. Weihe. On the differences between “practical” and “applied” (invited paper). In Proc. WAE 2000, Springer-Verlag LNCS 1982, pp. 1–10, 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alber, J., Fellows, M.R., Niedermeier, R. (2002). Efficient Data Reduction for Dominating Set: A Linear Problem Kernel for the Planar Case. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_16
Download citation
DOI: https://doi.org/10.1007/3-540-45471-3_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43866-3
Online ISBN: 978-3-540-45471-7
eBook Packages: Springer Book Archive