"1" . . "2"^^ . "0166-218X" . "rank-width; parameterized algorithms; graphs"@en . "276764" . "2"^^ . . "On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width"@en . "RIV/00216224:14330/10:00043472" . "On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width"@en . "14330" . "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 is linked to a work of Courcelle and Kant\u00E9 [7] who first proposed algebraic expressions with a so-called bilinear graph product as a better way of handling rank-decompositions, and to a parallel recent research of Bui-Xuan, Telle and Vatshelle."@en . "[A4812E1452FC]" . . "000276731700014" . "On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width" . . "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 is linked to a work of Courcelle and Kant\u00E9 [7] who first proposed algebraic expressions with a so-called bilinear graph product as a better way of handling rank-decompositions, and to a parallel recent research of Bui-Xuan, Telle and Vatshelle." . "P(GA201/08/0308), P(GC201/09/J021), S, Z(MSM0021622419)" . "RIV/00216224:14330/10:00043472!RIV11-GA0-14330___" . . "Hlin\u011Bn\u00FD, Petr" . . . . . "Ganian, Robert" . . . "Discrete Applied Mathematics" . . . . "17"^^ . . . "NL - Nizozemsko" . . . . "158" .