graph visualization based on rectangular dual gianluca quercini phd student disi – dipartimento di...

GRAPH VISUALIZATION BASED ON RECTANGULAR DUAL

Gianluca QuerciniPhD Student

Disi – Dipartimento di Informatica e Scienze dell'Informazione

Università degli Studi di Genova

Sydney, Wed November 21, 2007

Rectangular Dual

Lai & Leinwald

A graph admits a rectangular dual iff:

1) It is planar

2) Its internal faces are triangular

3) It does not contain separating triangles

Rectangular Dual of any Planar Graph

Kant & He, 1993Chiba & Nishizeki, 1985

Biedl, Kant, Kaufmann, 1995

Breaking the Separating Triangles

Problem: Adding a minimal set of crossover vertices to break all the separating triangles

A Polynomial Algorithm

Accornero, Ancona, Varini 2000

Towards a linear-time algorithm

Applications

3D Electronic Institutions

EI to 3D Worlds Rectangular dual

Cartograms

Weighted Rectangular Dual

Graph Drawing

Goal: to obtain a pleasant drawing

Large graphs

3D Graph Drawing

Fish-eye lens

Clustering

Traditional graph drawing representations Rectangular Dual

Clustering by Rectangular Dualization