Abstract
Graph drawing algorithms based on minimizing the so-called stress energy strive to place nodes in accordance with target distances. They were first introduced to the graph drawing field by Kamada and Kawai [11], and they had previously been used to visualize general kinds of data by multidimensional scaling. In this paper we suggest a novel algorithm for the minimization of the Stress energy. Unlike prior stress-minimization algorithms, our algorithm is suitable for a one-dimensional layout, where one axis of the drawing is already given and an additional axis needs to be computed. This 1-D drawing capability of the algorithm is a consequence of replacing the traditional node-by-node optimization with a more global axis-by-axis optimization. Moreover, our algorithm can be used for multidimensional graph drawing, where it has time and space complexity advantages compared with other stress minimization algorithms.
Chapter PDF
Similar content being viewed by others
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.
References
Carmel, L., Harel, D., Koren, Y.: Drawing Directed Graphs Using One-Dimensional Optimization. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 193–206. Springer, Heidelberg (2002)
Carmel, L., Harel, D., Koren, Y.: Combining Hierarchy and Energy for Drawing Directed Graphs. IEEE Transactions on Visualization and Computer Graphics, IEEE (in press)
Cohen, J.D.: Drawing Graphs to Convey Proximity: an Incremental Arrangement Method. ACM Transactions on Computer-Human Interaction 4, 197–229 (1997)
Gajer, P., Goodrich, M.T., Kobourov, S.G.: A Multi-dimensional Approach to Force-Directed Layouts of Large Graphs. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 211–221. Springer, Heidelberg (2001)
Hadany, R., Harel, D.: A Multi-Scale Method for Drawing Graphs Nicely. Discrete Applied Mathematics 113, 3–21 (2001)
Harel, D., Koren, Y.: A Fast Multi-Scale Method for Drawing Large Graphs. Journal of Graph Algorithms and Applications 6, 179–202 (2002)
Harel, D., Koren, Y.: Graph Drawing by High-Dimensional Embedding. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 207–219. Springer, Heidelberg (2002)
Koren, Y., Carmel, L., Harel, D.: ACE: A Fast Multiscale Eigenvectors Computation for Drawing Huge Graphs. In: Proc. IEEE Information Visualization (InfoVis 2002), pp. 137–144. IEEE, Los Alamitos (2002)
Koren, Y., Harel, D.: One-Dimensional Graph Drawing: Part I — Drawing Graphs by Axis Separation. Technical report MCS03-08, Faculty of Math. and Computer Science, The Weizmann Institute of Science (2003)
Koren, Y.: Graph Drawing by Subspace Optimization (to be published)
Kamada, T., Kawai, S.: An Algorithm for Drawing General Undirected Graphs. Information Processing Letters 31, 7–15 (1989)
Sammon, J.W.: A Nonlinear Mapping for Data Structure Analysis. IEEE Trans. on Computers 18, 401–409 (1969)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Koren, Y., Harel, D. (2004). Axis-by-Axis Stress Minimization. In: Liotta, G. (eds) Graph Drawing. GD 2003. Lecture Notes in Computer Science, vol 2912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24595-7_42
Download citation
DOI: https://doi.org/10.1007/978-3-540-24595-7_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20831-0
Online ISBN: 978-3-540-24595-7
eBook Packages: Springer Book Archive