Antonios Symvonis

Boundary labeling: Models and efficient algorithms for rectangular maps

We introduce boundary labeling, a new model for labeling point sites with large labels. According to the boundary-labeling model, labels are placed around an axis-parallel rectangle that contains the point sites, each label is connected to its corresponding site through a polygonal line called leader, and no two leaders intersect. Although boundary labeling is commonly used, e.g., for technical drawings and illustrations in medical atlases, this problem has not yet been studied in the literature. The problem is interesting in that it is a mixture of a label-placement and a graph-drawing problem. In this paper we investigate several variants of the boundary-labeling problem. We consider labels of identical or different size, straight-line or rectilinear leaders, fixed or sliding ports for attaching leaders to sites and attaching labels to one, two or all four sides of the bounding rectangle. For any variant of the boundary labeling model, we aim at highly esthetical placements of labels and leaders. We present simple and efficient algorithms that minimize the total leader length or, in the case of rectilinear leaders, the total number of bends.

Drawing graphs in the plane with high resolution

This paper presents the problem of drawing a graph in the plane so that edges appear as straight lines and the minimum angle formed by any pair of incident edges is maximized. The resolution of a layout is defined to be the size of the minimum angle formed by incident edges of the graph, and the resolution of a graph to be the maximum resolution of any layout of the graph. The resolution R of a graph is characterized in terms of the maximum node degree d of the graph by proving that

Three-dimensional orthogonal graph drawing algorithms

\Omega (\frac{1}{{d^2 }}) \leqslant R \leqslant \frac{{2\pi }}{d}

Two Algorithms for Three Dimensional Orthogonal Graph Drawing

for any graph. Moreover, it is proved that

Boundary Labeling with Octilinear Leaders

R = \Theta (\frac{1}{d})

Boundary labeling: models and efficient algorithms for rectangular maps

for many graphs including planar graphs, complete graphs, hypercubes, multidimensional meshes and tori, and other special networks. It is also shown that the problem of deciding if

The straight-line RAC drawing problem is NP-hard

R = \frac{{2\pi }}{d}

On the perspectives opened by right angle crossing drawings

for a graph is NP-hard for

Optimal stable merging

d = 4

Fan-planarity

, and by using a counting argument that