DMCA
Bidimensionality and Kernels (2010)
| Citations: | 58 - 23 self |
BibTeX
@MISC{Fomin10bidimensionalityand,
author = {Fedor V. Fomin and Daniel Lokshtanov and Saket Saurabh and Dimitrios M. Thilikos},
title = {Bidimensionality and Kernels},
year = {2010}
}
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Abstract
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
Keyphrases
bidimensionality theory linear kernel parameterized problem bidimensional problem third meta-algorithmic direction polynomial time algorithm h-minor free graph powerful framework sub-exponential time polynomial time approximation scheme hajiaghayi soda meta-algorithmic technique problem instance parameterized complexity
