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GRAPH VISUALIZATION BASED ON RECTANGULAR DUAL Gianluca Quercini PhD Student Disi – Dipartimento di Informatica e Scienze dell'Informazione Università degli Studi di Genova Sydney, Wed November 21, 2007

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Rectangular Dual

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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

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Rectangular Dual of any Planar Graph Kant & He, 1993Chiba & Nishizeki, 1985 Biedl, Kant, Kaufmann, 1995

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

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A Polynomial Algorithm Accornero, Ancona, Varini 2000

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Towards a linear-time algorithm

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Applications

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3D Electronic Institutions EI to 3D Worlds Rectangular dual

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Cartograms Weighted Rectangular Dual

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Graph Drawing Goal: to obtain a pleasant drawing Large graphs 3D Graph Drawing Fish-eye lens Clustering Traditional graph drawing representations Rectangular Dual

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Clustering by Rectangular Dualization

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