Abstract
Algorithmic meta-theorems are algorithmic results that apply to a whole range of problems, instead of addressing just one specific problem. This kind of theorems are often stated relative to a certain class of graphs, so the general form of a meta theorem reads “every problem in a certain class 
of problems can be solved efficiently on every graph satisfying a certain property 
”. A particularly well known example of a meta-theorem is Courcelle’s theorem that every decision problem definable in monadic second-order logic (MSO) can be decided in linear time on any class of graphs of bounded tree-width [1].
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
Courcelle, B.: Graph rewriting: An algebraic and logic approach. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, pp. 194–242. Elsevier, Amsterdam (1990)
Courcelle, B., Makowsky, J., Rotics, U.: Linear time solvable optimization problems on graphs of bounded clique-width. Theory Comput. Systems 33, 125–150 (2000)
Dawar, A., Grohe, M., Kreutzer, S.: Locally excluding a minor. In: Proc. of the 22nd IEEE Symp. on Logic in Computer Science, pp. 270–279 (2007)
Dawar, A., Grohe, M., Kreutzer, S., Schweikardt, S.: Approximation schemes for first-order definable optimisation problems. In: Proc. of the 21st IEEE Symp. on Logic in Computer Science, pp. 411–420 (2006)
Demaine, E., Hajiaghayi, M., Kawarabayashi, K.: Algorithmic graph minor theory: Decomposition, approximation, and coloring. In: Symposium on Foundations of Computer Science (FOCS), pp. 637–646 (2005)
Flum, J., Grohe, M.: Fixed-parameter tractability, definability, and model checking. SIAM Journal on Computing 31, 113–145 (2001)
Frick, M., Grohe, M.: Deciding first-order properties of locally tree-decomposable structures. Journal of the ACM 48, 1184–1206 (2001)
Grohe, M.: Logic, graphs, and algorithms. In: Wilke, T., Flum, J., Grädel, E. (eds.) Logic and Automata History and Perspectives, Amsterdam University Press (2007)
Khanna, S., Motwani, R.: Towards a syntactic characterization of PTAS. In: Proc. of STOC 1996, pp. 329–337 (1996)
Kolaitis, P.G., Thakur, M.N.: Logical definability of NP optimization problems. Information and Computation 115(2), 321–353 (1994)
Kolaitis, P.G., Thakur, M.N.: Approximation properties of NP minimization classes. Journal of Computer and System Sciences 50, 391–411 (1995)
Kreutzer, S.: Finite model-theory of tree-like structures, http://web.comlab.ox.ac.uk/oucl/work/stephan.kreutzer/publications.html
Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. Journal of Computer and System Sciences 43, 425–440 (1991)
Seese, D.: Linear time computable problems and first-order descriptions. Mathematical Structures in Computer Science 2, 505–526 (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kreutzer, S. (2008). Algorithmic Meta-theorems. In: Grohe, M., Niedermeier, R. (eds) Parameterized and Exact Computation. IWPEC 2008. Lecture Notes in Computer Science, vol 5018. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79723-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-79723-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79722-7
Online ISBN: 978-3-540-79723-4
eBook Packages: Computer ScienceComputer Science (R0)