Computing straight-line 3D grid drawings of graphs in linear volume

Authors:
Emilio Di Giacomo;Giuseppe Liotta;Henk Meijer
Affiliations:
Dipartimento di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia, Perugia, Italy;Dipartimento di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia, Perugia, Italy;Department of Computing and Information Science, Queen's University, Kingston, Ontario, Canada
Venue:
Computational Geometry: Theory and Applications
Year:
2005

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Abstract

This paper investigates the basic problem of computing crossing-free straight-line 3D grid drawings of graphs such that the overall volume is small. Motivated by their relevance in the literature, we focus on families of graphs having constant queue number and on k-trees. We present algorithms that compute drawings of these families of graphs on 3D grids consisting of a constant number of parallel lines and such that the overall volume is linear. Lower bounds on the number of such grid lines are also provided. Our results extend and improve similar ones already described in the literature.