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Computational Geometry
Volume 32, Issue 1, September 2005, Pages 26-58
 
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doi:10.1016/j.comgeo.2004.11.003    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2005 Elsevier B.V. All rights reserved.

Computing straight-line 3D grid drawings of graphs in linear volumestar, open

Emilio Di Giacomoa, Corresponding Author Contact Information, E-mail The Corresponding Author, Giuseppe Liottaa, E-mail The Corresponding Author and Henk Meijerb, E-mail The Corresponding Author

aDipartimento di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia, Perugia, Italy bDepartment of Computing and Information Science, Queen's University, Kingston, Ontario, Canada

Received 12 December 2003; 
revised 11 November 2004; 
accepted 18 November 2004. 
Communicated by D. Wagner. 
Available online 4 May 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.

Keywords: Three-dimensional graph drawing; Track layout; Straight-line drawings


Computational Geometry
Volume 32, Issue 1, September 2005, Pages 26-58
 
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