Automata-formalization for graphs of bounded rank-width

Bc. Robert Ganian

Master's thesis

Abstract:

Rank-width is a new structural measure of graphs introduced by Oum and Seymour. The outcome of this work is to define and prove a "parse-tree" characterization of the graphs of bounded rank-width, and a corresponding analogue of the Myhill-Nerode theorem. (Similar characterizations exist, e.g. for the graphs of bounded tree-width or bounded branch-width.) This effort aims at creating a schematic framework for design of efficient algorithms on graphs of bounded rank-width, using the tools of automata theory.

Abstract:

Rank-width is a new structural measure of graphs introduced by Oum and Seymour. The outcome of this work is to define and prove a "parse-tree" characterization of the graphs of bounded rank-width, and a corresponding analogue of the Myhill-Nerode theorem. (Similar characterizations exist, e.g. for the graphs of bounded tree-width or bounded branch-width.) This effort aims at creating a schematic framework for design of efficient algorithms on graphs of bounded rank-width, using the tools of automata theory.

Keywords

Rank-width, Parse trees, Tree automata, Graphs of bounded Rank-width

Language used: English

Date on which the thesis was submitted / produced: 22. 5. 2008

Thesis defence

• Date of defence: 1. 7. 2008
• Supervisor: prof. RNDr. Petr Hliněný, Ph.D.
• Reader: doc. Mgr. Jan Obdržálek, PhD.

Masaryk University

Faculty of Informatics

Master programme / field:
Informatics / Theoretical Informatics