An Efficient Implementation of Sugiyama's Algorithm for Layered Graph Drawing
Eiglsperger, Markus and Siebenhaller, Martin and Kaufmann, Michael (2004) An Efficient Implementation of Sugiyama's Algorithm for Layered Graph Drawing. In: Graph Drawing 12th International Symposium, GD 2004, September 29-October 2, 2004, New York, NY, USA , pp. 155-166 (Official URL: http://dx.doi.org/10.1007/978-3-540-31843-9_17).
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Sugiyama's algorithmic framework for layered graph drawing is commonly used in practical software. The extensive use of dummy vertices to break long edges between non-adjacent layers often leads to unsatisfactorial performance. The worst-case running-time of Sugiyamarsquos approach is O(|V||E|\log|E|) requiring O(|V||E|) memory, which makes it unusable for the visualization of large graphs. By a conceptually simple new technique we are able to keep the number of dummy vertices and edges linear in the size of the graph and hence reduce the worst-case time complexity of Sugiyamarsquos approach by an order of magnitude to O((|V|+|E|)\log|E|) requiring O(|V|+|E|) space. This work has partially been supported by the DFG-grant Ka512/8-2. It has been performed when the first author was with the Universität Tübingen.
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