Bidimensionality and Kernels

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Bidimensionality and Kernels
Bidimensionality theory appears to be a powerful framework in the development of meta-algorithmic techniques. It was introduced by Demaine et al. [J. ACM 2005 ] as a tool to obtain sub-exponential time parameterized algorithms for bidimensional problems on H-minor free graphs. Demaine and Hajiaghayi [SODA 2005 ] extended the theory to obtain polynomial time approximation schemes (PTASs) for bidimensional problems. In this paper, we establish a third meta-algorithmic direction for bidimensionality theory by relating it to the existence of linear kernels for parameterized problems. In parameterized complexity, each problem instance comes with a parameter k and the parameterized problem is said to admit a linear kernel if there is a polynomial time algorithm, called a kernelization algorithm, that reduces the input instance to an equivalent instance (called kernel) with size linearly bounded by k. We show that "essentially" all bidimensional problems not only have sub-exponenti...
Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh,
Added 01 Mar 2010
Updated 02 Mar 2010
Type Conference
Year 2010
Where SODA
Authors Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, Dimitrios M. Thilikos
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