Bidimensionality and geometric graphs

Bidimensionality theory was introduced by Demaine et al. [JACM 2005 ] as a framework to obtain algorithmic results for hard problems on minor closed graph classes. The theory has been sucessfully applied to yield subexponential time parameterized algorithms, EPTASs and linear kernels for many problems on families of graphs excluding a fixed graph H as a minor. In this paper we use several of the key ideas from Bidimensionality to give a new generic approach to design EPTASs and subexponential time parameterized algorithms for problems on classes of graphs which are not minor closed, but instead exhibit a geometric structure. In particular we present EPTASs and subexponential time parameterized algorithms for FEEDBACK VERTEX SET, VERTEX COVER, CONNECTED VERTEX COVER, DIAMOND HITTING SET, on map graphs and unit disk graphs, and for CYCLE PACKING and MINIMUM-VERTEX FEEDBACK EDGE SET on unit disk graphs. To the best of our knowledge, these results were previously unknown, with the except...

• Type: Journal
• Year: 2012
• Where: SODA
• Authors: Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh
• Keywords: Algorithms, Feedback Vertex, Intersection Graphs, SODA 2012, Unit Disk Graphs