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13
Optimal Leaf Ordering for Two and a Half Dimensional Phylogenetic Tree Visualisation
, 2004
"... Two and a half dimensional graph visualisation is the stacking of a set of related graphs, each drawn in a plane, into the third dimension to support visual comparison. A new aesthetic criterion is introduced for the 2 D visualisation of sets of related phylogenetic trees. This aesthetic requires ..."
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Cited by 13 (3 self)
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Two and a half dimensional graph visualisation is the stacking of a set of related graphs, each drawn in a plane, into the third dimension to support visual comparison. A new aesthetic criterion is introduced for the 2 D visualisation of sets of related phylogenetic trees. This aesthetic requires that the number of crossings between edges linking similar nodes in adjacent trees is minimised allowing a user to easily track the position of a particular species through its lifetime in the stack. We introduce an algorithm for e#ciently minimising such crossings and discuss its complexity. Finally, we suggest a new "barrel" layout style which benefits from such crossing minimisation.
An Efficient Implementation of Sugiyama’s Algorithm for Layered Graph Drawing
 JOURNAL OF GRAPH ALGORITHMS AND APPLICATIONS
, 2005
"... Sugiyama’s algorithm for layered graph drawing is very popular and commonly used in practical software. The extensive use of dummy vertices to break long edges between nonadjacent layers often leads to unsatisfying performance. The worstcase runningtime of Sugiyama’s approach is O(V E  log E ..."
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Cited by 9 (2 self)
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Sugiyama’s algorithm for layered graph drawing is very popular and commonly used in practical software. The extensive use of dummy vertices to break long edges between nonadjacent layers often leads to unsatisfying performance. The worstcase runningtime of Sugiyama’s 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 without increasing the number of crossings. We reduce the worstcase time complexity of Sugiyama’s approach by an order of magnitude to O((V  + E) log E) requiring O(V  + E) space.
Confluent layered drawings
 IN GRAPH DRAWING (PROC. GD ’04)
, 2004
"... We combine the idea of confluent drawings with Sugiyama style drawings, in order to reduce the edge crossings in the resultant drawings. Furthermore, it is easier to understand the structures of graphs from the mixed style drawings. The basic idea is to cover a layered graph by complete bipartite s ..."
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Cited by 7 (3 self)
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We combine the idea of confluent drawings with Sugiyama style drawings, in order to reduce the edge crossings in the resultant drawings. Furthermore, it is easier to understand the structures of graphs from the mixed style drawings. The basic idea is to cover a layered graph by complete bipartite subgraphs (bicliques), then replace bicliques with treelike structures. The biclique cover problem is reduced to a special edge coloring problem and solved by heuristic coloring algorithms. Our method can be extended to obtain multidepth confluent layered drawings.
Drawing graphs with glee
, 2007
"... Abstract. This paper describes novel methods we developed to lay out graphs using Sugiyama’s scheme [16] in a tool named GLEE. The main contributions are: a heuristic for creating a graph layout with a given aspect ratio, an efficient method of edgecrossings counting while performing adjacent verte ..."
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Cited by 5 (2 self)
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Abstract. This paper describes novel methods we developed to lay out graphs using Sugiyama’s scheme [16] in a tool named GLEE. The main contributions are: a heuristic for creating a graph layout with a given aspect ratio, an efficient method of edgecrossings counting while performing adjacent vertex swaps, and a simple and fast spline routing algorithm. 1
The Barycenter Heuristic and the Reorderable Matrix
, 2005
"... this paper is to discuss the role of the barycenter heuristic in ordering the rows and columns of the matrix. So far, the barycenter heuristic has been mainly used in graph drawing algorithms. In order to gain full advantage of the barycenter heuristic in ordering rows and columns of the reorderable ..."
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Cited by 3 (0 self)
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this paper is to discuss the role of the barycenter heuristic in ordering the rows and columns of the matrix. So far, the barycenter heuristic has been mainly used in graph drawing algorithms. In order to gain full advantage of the barycenter heuristic in ordering rows and columns of the reorderable matrix, we survey its use in various contexts and recall the theoretical results obtained
Grid Sifting: Leveling and Crossing Reduction
, 2011
"... Directed graphs are commonly drawn by the Sugiyama algorithm where first vertices are placed on distinct hierarchical levels and second the vertices on the same level are permuted to reduce the overall number of crossings. Separating these two phases simplifies the algorithms but diminishes the qual ..."
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Cited by 3 (1 self)
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Directed graphs are commonly drawn by the Sugiyama algorithm where first vertices are placed on distinct hierarchical levels and second the vertices on the same level are permuted to reduce the overall number of crossings. Separating these two phases simplifies the algorithms but diminishes the quality of the result. We introduce a combined leveling and crossing reduction algorithm based on sifting, which prioritizes few crossings over few levels. It avoids type 2 conflicts which help to straighten the edges, and has a running time, which is roughly quadratic in the size of the input graph independent of dummy vertices.
Barcelona Aarhus Barcelona
, 2002
"... This is the second annual progress report for the ALCOMFT project, supported by the European ..."
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This is the second annual progress report for the ALCOMFT project, supported by the European