Faster Force-Directed Graph Drawing with the Well-Separated Pair Decomposition

doi:10.3390/a9030053

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force-directed graph drawing

well-separated pair decomposition

Fruchterman–Reingold algorithm

experiments

number of crossings

deviation of edge lengths

runtime

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Open AccessArticle

Algorithms 2016, 9(3), 53; doi:10.3390/a9030053

Faster Force-Directed Graph Drawing with the Well-Separated Pair Decomposition^†

Fabian Lipp *

, Alexander Wolff

and Johannes Zink

Lehrstuhl für Informatik I, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany

^†

This paper is an extended version of our paper published in Proceedings of the 23rd International Symposium on Graph Drawing and Network Visualization (GD 2015), Los Angeles, CA, USA, 24–26 September 2015.

Author to whom correspondence should be addressed.

Academic Editor: Maurizio Patrignani

Received: 24 December 2015 / Revised: 15 July 2016 / Accepted: 15 July 2016 / Published: 4 August 2016

(This article belongs to the Special Issue Graph Drawing and Experimental Algorithms)

View Full-Text | Download PDF [14805 KB, uploaded 4 August 2016] |

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Abstract

The force-directed paradigm is one of the few generic approaches to drawing graphs. Since force-directed algorithms can be extended easily, they are used frequently. Most of these algorithms are, however, quite slow on large graphs, as they compute a quadratic number of forces in each iteration. We give a new algorithm that takes only

O (m + n log n)

time per iteration when laying out a graph with n vertices and m edges. Our algorithm approximates the true forces using the so-called well-separated pair decomposition. We perform experiments on a large number of graphs and show that we can strongly reduce the runtime, even on graphs with less than a hundred vertices, without a significant influence on the quality of the drawings (in terms of the number of crossings and deviation in edge lengths). View Full-Text

Keywords: force-directed graph drawing; well-separated pair decomposition; Fruchterman–Reingold algorithm; experiments; number of crossings; deviation of edge lengths; runtime force-directed graph drawing; well-separated pair decomposition; Fruchterman–Reingold algorithm; experiments; number of crossings; deviation of edge lengths; runtime

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Lipp, F.; Wolff, A.; Zink, J. Faster Force-Directed Graph Drawing with the Well-Separated Pair Decomposition. Algorithms 2016, 9, 53.

AMA Style

Lipp F, Wolff A, Zink J. Faster Force-Directed Graph Drawing with the Well-Separated Pair Decomposition. Algorithms. 2016; 9(3):53.

Chicago/Turabian Style

Lipp, Fabian; Wolff, Alexander; Zink, Johannes. 2016. "Faster Force-Directed Graph Drawing with the Well-Separated Pair Decomposition." Algorithms 9, no. 3: 53.

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