Abstract
Horizontal placement of nodes in tree layout or layered drawings of directed graphs can be modelled as a convex quadratic program. Thus, quadratic programming provides a declarative framework for specifying such layouts which can then be solved optimally with a standard quadratic programming solver. While slower than specialized algorithms, the quadratic programming approach is fast enough for practical applications and has the great benefit of being flexible yet easy to implement with standard mathematical software. We demonstrate the utility of this approach by using it to layout hi-trees. These are a tree-like structure with compound nodes recently introduced for visualizing the logical structure of arguments and of decisions.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dwyer, T., Koren, Y., Marriott, K.: IPSep-CoLa: An incremental procedure for separation constraint layout of graphs. IEEE Transactions on Visualization and Computer Graphics 12(5), 821–828 (2006)
Dwyer, T., Koren, Y., Marriott, K.: Drawing directed graphs using quadratic programming. IEEE Transactions on Visualization and Computer Graphics 12(4), 536–548 (2006)
He, W., Marriott, K.: Constrained graph layout. Constraints 3, 289–314 (1998)
Bohanec, M.: DEXiTree: A program for pretty drawing of trees. In: Proc. Information Society IS 2007, pp. 8–11 (2007)
Marriott, K., Stuckey, P., Tam, V., He, W.: Removing node overlapping in graph layout using constrained optimization. Constraints 8, 143–171 (2003)
Dwyer, T., Marriott, K., Stuckey, P.J.: Fast node overlap removal. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 153–164. Springer, Heidelberg (2006)
Goldfarb, D., Idnani, A.: A numerically stable dual method for solving strictly convex quadratic programs. Mathematical Programming 26, 1–33 (1983)
Marriott, K., Sbarski, P., Gelder, T., Prager, D., Bulka, A.: Hi-Trees and Their Layout. IEEE Transactions on Visualization and Computer Graphics (to appear)
Sbarski, P., Gelder, T., Marriott, K., Prager, D., Bulka, A.: Visualizing Argument Structure. In: Proceedings of the 4th International Symposium on Advances in Visual Computing, pp. 129–138 (2008)
Walker I, J.Q.: A node-positioning algorithm for general trees. Softw. Pract. Exper. 20(7), 685–705 (1990)
Reingold, E.M., Tilford, J.S.: Tidier drawings of trees. IEEE Transactions on Software Engineering 7(2), 223–228 (1981)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dwyer, T., Marriott, K., Sbarski, P. (2010). Hi-tree Layout Using Quadratic Programming. In: Goel, A.K., Jamnik, M., Narayanan, N.H. (eds) Diagrammatic Representation and Inference. Diagrams 2010. Lecture Notes in Computer Science(), vol 6170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14600-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-14600-8_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14599-5
Online ISBN: 978-3-642-14600-8
eBook Packages: Computer ScienceComputer Science (R0)