Annual Report 2010 - Fachgruppe Informatik an der RWTH Aachen ...

The major goal of this project is to close this gap and implement algorithms for Courcelle's
Theorem that can compete with specific algorithms for the respective problems. Due to the
hardness and complexity of the underlying model-checking problem with non-elementary
lower-bounds, a naive and straight-forward implementation will most probably not be of any
practical relevance. Therefore, this task includes inventing new advanced techniques to
circumvent the arising difficulties and obstacles.
Structural Graph Theory and Parameterized Complexity
Somnath Sikdar, Joachim Kneis, Peter Rossmanith
Funded by the DFG-GACR Bilateral Project Program, grant RO 927/9
Many real-world algorithmic problems turn out to be intractable in their full generality.
Parameterized complexity, however, provides a useful framework for a refined analysis of
such hard problems, and a new concept in designing algorithms that can solve hard problems
for real-world instances efficiently. In contrast to heuristics, this approach provides
guaranteed runtime bounds.
Graphs are combinatorial structures suitable for modeling many discrete decision and
optimization problems. Structural graph theory has already proven very useful in
parameterized algorithmics. For instance, most of the traditional hard problems are efficiently
solvable on graphs of bounded tree-width.
In this project, we plan to exploit further structural properties of graphs like branch-width,
DAG-width, rank-width, or their topological properties. Our goal is to find new application
areas of structural graph theory in parameterized algorithm design.
Parameterized Algorithms & Property Testing
Joachim Kneis, Alexander Langer, Peter Rossmanith
Funded by the DFG-NSC Bilateral Project Program
In real world applications, we often have to deal with huge data sets quickly and often we
want to decide whether a given data set has a certain property. In practice, it is often
sufficient to know whether the data set probably has a given property, or that the data set is at
least close to having this property. For optimization problems, we could use approximation
algorithms for a quick estimate of the solution. However, properties, such as ‘Is the data set
sorted?’, either hold or do not hold, and hence they cannot be approximated, since there is to
approximation to a ‘yes’ or ‘no’ answer.
This has lead to the concept of property testing: A property testing algorithm should be very
fast and answer ‘yes’ if the property holds, and should answer ‘no'’ if the input is ‘far away’
from having the property. Ideally, such property testers might test instances in sublinear time
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