A Layout algorithm for data flow diagrams
IEEE Transactions on Software Engineering
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Integer and combinatorial optimization
Integer and combinatorial optimization
An experimental comparison of four graph drawing algorithms
Computational Geometry: Theory and Applications
Turn-regularity and optimal area drawings of orthogonal representations
Computational Geometry: Theory and Applications
On the complexity of the edge label placement problem
Computational Geometry: Theory and Applications
On the complexity of orthogonal compaction
Computational Geometry: Theory and Applications
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Numerical Experience with Lower Bounds for MIQP Branch-And-Bound
SIAM Journal on Optimization
Software—Practice & Experience
Drawing High Degree Graphs with Low Bend Numbers
GD '95 Proceedings of the Symposium on Graph Drawing
Placing edge labels by modifying an orthogonal graph drawing
GD'10 Proceedings of the 18th international conference on Graph drawing
A mixed-integer program for drawing high-quality metro maps
GD'05 Proceedings of the 13th international conference on Graph Drawing
DAGView: an approach for visualizing large graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
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This paper studies the problem of computing orthogonal drawings of graphs with labels on vertices and edges. Our research is mainly motivated by Software Engineering and Information Systems domains, where tools like UML diagrams and ER-diagrams are considered fundamental for the design of sophisticated systems and/or complex data bases collecting enormous amount of information. A label is modeled as a rectangle of prescribed width and height and it can be associated with either a vertex or an edge. Our drawing algorithms guarantee no overlaps between labels, vertices, and edges and take advantage of the information about the set of labels to compute the geometry of the drawing. Several additional optimization goals are taken into account. Namely, the labeled drawing can be required to have either minimum total edge length, or minimum width, or minimum height, or minimum area among those preserving a given orthogonal representation. All these goals lead to NP-hard problems. We present MILP models to compute optimal drawings with respect to the first three goals and an exact algorithm that is based on these models to compute a labeled drawing of minimum area. We also present several heuristics for computing compact labeled orthogonal drawings and experimentally validate their performances, comparing their solutions against the optimum.