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...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, Dimitrios M. Thilikos
• Keywords: Discrete Algorithms, Linear Kernels, Parameterized Problems, SODA 2010, Time Parameterized Algorithms