Bidimensionality and EPTAS

Bidimensionality theory appears to be a powerful framework for the development of metaalgorithmic techniques. It was introduced by Demaine et al. [J. ACM 2005 ] as a tool to obtain sub-exponential time parameterized algorithms for problems on H-minor free graphs. Demaine and Hajiaghayi [SODA 2005 ] extended the theory to obtain polynomial time approximation schemes (PTASs) for bidimensional problems, and subsequently improved these results to EPTASs. Fomin et. al [SODA 2010 ] established a third meta-algorithmic direction for bidimensionality theory by relating it to the existence of linear kernels for parameterized problems. In this paper we revisit bidimensionality theory from the perspective of approximation algorithms and redesign the framework for obtaining EPTASs to be more powerful, easier to apply and easier to understand. Two of the most widely used approaches to obtain PTASs on planar graphs are the LiptonTarjan separator based approach [SICOMP 1980 ], and Baker's appro...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh
• Keywords: Bidimensional Problems, Bidimensionality Theory, CORR 2010, Education, Problems