On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width

Rank-width is a structural graph measure introduced by Oum and Seymour and aimed at better handling of graphs of bounded clique-width. We propose a formal mathematical framework and tools for easy design of dynamic algorithms running directly on a rankdecomposition of a graph (on contrary to the usual approach which translates a rank-decomposition into a clique-width expression, with a possible exponential jump in the parameter). The main advantage of this framework is a fine control over the runtime dependency on the rank-width parameter. Our new approach links to a work of Courcelle and Kant

• Type: Journal
• Year: 2010
• Where: DAM
• Authors: Robert Ganian, Petr Hlinený
• Keywords: DAM 2010, Formal Mathematical Framework, Possible Exponential Jump, Structural Graph Measure