Bidimensionality

Bidimensionality theory characterizes a broad range of graph problems (bidimensional) that admit efficient approximate, fixed-parameter or kernel solutions in a broad range of graphs. These graph classes include planar graphs, map graphs, bounded-genus graphs and graphs excluding any fixed minor. In particular, bidimensionality theory builds on the graph minor theory of Robertson and Seymour by extending the mathematical results and building new algorithmic tools. The theory was introduced in the work of Demaine, Fomin, Hajiaghayi, and Thilikos, for which the authors received the Nerode Prize in 2015.

A parameterized problem ${\displaystyle \Pi }$ is a subset of ${\displaystyle \Gamma ^{*}\times \mathbb {N} }$ for some finite alphabet ${\displaystyle \Gamma }$. An instance of a parameterized problem consists of (x,k), where k is called the parameter.

...
Wikipedia