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Upward Graph Drawing

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Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

1994; Bertolazzi, Di Battista, Liotta, Mannino

Problem Definition

Upward graph drawing is concerned with computing two-dimensional layouts of directed graphs where all edges flow in the upward direction. Namely, given a directed graph G(V, E) (also called a digraph for short), an upward drawing of G is a drawing such that: (i) each vertex v ∈ V is mapped to a distinct point p v of the plane and (ii) each edge (u, v) ∈ E is drawn as a simple curve from p u and p v , monotonically increasing in the upward direction.

Clearly, G admits an upward drawing only if it does not contain directed cycles; if we allow edge crossings, acyclicity is also a sufficient condition for the existence of an upward drawing. Instead, if G is planar and we require that also the upward drawing of G is crossing-free, acyclicity is only a necessary condition, and the upward drawability of Gbecomes a much more intriguing problem. An upward drawing with no edge...

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Recommended Reading

  1. Bertolazzi P, Di Battista G, Didimo W (2002) Quasi-upward planarity. Algorithmica 32(3):474–506

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  2. Bertolazzi P, Di Battista G, Liotta G, Mannino C (1994) Upward drawings of triconnected digraphs. Algorithmica 12(6):476–497

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  3. Chimani M, Gutwenger C, Jünger M, Klau GW, Klein K, Mutzel P (2013) The open graph drawing framework (OGDF). In: Tamassia R (ed) Handbook of graph drawing and visualization. CRC Press - Taylor & Francis Group Boca Raton, FL, USA

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  4. Chimani M, Zeranski R (2013) Upward planarity testing: a computational study. In: Proceedings of Graph Drawing (GD’13), Bordeaux. Volume 8242 of LNCS. Springer, pp 13–24

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  5. Di Battista G, Didimo W (2013) GDToolkit. In: Tamassia R (ed) Handbook of graph drawing and visualization. CRC Press - Taylor & Francis Group Boca Raton, FL, USA

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  6. Di Battista G, Eades P, Tamassia R, Tollis IG (1998) Graph drawing: algorithms for the visualization of graphs. Prentice Hall, Upper Saddle River, New Jersey, USA

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  7. Di Battista G, Tamassia R (1988) Algorithms for plane representations of acyclic digraphs. Theor Comput Sci 61:175–198

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  8. Didimo W, Giordano F, Liotta G (2009) Upward spirality and upward planarity testing. SIAM J Discret Math 23(4):1842–1899

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  9. Garg A, Tamassia R (1992) On the computational complexity of upward and rectilinear planarity testing. SIAM J Comput 31(2):601–625

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Author information

Authors and Affiliations

  1. Department of Engineering, University of Perugia, Perugia, Italy

    Walter Didimo

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  1. Walter Didimo
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Correspondence to Walter Didimo .

Editor information

Editors and Affiliations

  1. Dept. Electrical Engineering & Computer Science, Northwestern University, Evanston, Illinois, USA

    Ming-Yang Kao

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Didimo, W. (2015). Upward Graph Drawing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27848-8_653-1

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  • DOI: https://doi.org/10.1007/978-3-642-27848-8_653-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Online ISBN: 978-3-642-27848-8

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