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Graph Layout through the VCG Tool
, 1994
"... The VCG tool allows the visualization of graphs that occur typically as data structures in programs. We describe the functionality of the VCG tool, its layout algorithm and its heuristics. Our main emphasis in the selection of methods is to achieve a very good performance for the layout of large gra ..."
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Cited by 53 (0 self)
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The VCG tool allows the visualization of graphs that occur typically as data structures in programs. We describe the functionality of the VCG tool, its layout algorithm and its heuristics. Our main emphasis in the selection of methods is to achieve a very good performance for the layout of large graphs. The tool supports the partitioning of edges and nodes into edge classes and nested subgraphs, the folding of regions, and the management of priorities of edges. The algorithm produces good drawings and runs reasonably fast even on very large graphs.
Upper bounds on the number of hidden nodes in the Sugiyama algorithm
 In GD ’96: Proceedings of the Symposium on Graph Drawing, volume 1190 of LNCS
, 1997
"... The Sugiyama algorithm is a wellknown techique for drawing arbitrary directed grapds G=(V,E). It is being widely used in current graphdrawing systems. Despite its importance and widespread use, little is known about the time and space complexity of several parts of the algorithm. This paper impro ..."
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Cited by 2 (0 self)
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The Sugiyama algorithm is a wellknown techique for drawing arbitrary directed grapds G=(V,E). It is being widely used in current graphdrawing systems. Despite its importance and widespread use, little is known about the time and space complexity of several parts of the algorithm. This paper improves this situation by analyzing the exact and asymptotic worstcase complexity of the simplification phase of the Sugiyama algorithm. This complexity is dominated by the number d of added invisible (a.k.a. hidden or dummy) nodes. The best previously known upper bound for this number is O(min{V^3,E^2}). We connect both partial results and show that d can be expressed a function d(h,n,m) of the height h of the underlying layering, the number of vertices n=V and the number of edgeds E. We analyze d(h,n,m) and improve on the previously known bounds by giving a closedform description and sharp asymptotic bounds for several relevant cases.