Ulrich Fößmeier

Drawing High Degree Graphs with Low Bend Numbers

We consider the problem of drawing plane graphs with an arbitrarily high vertex degree orthogonally into the plane such that the number of bends on the edges should be minimized. It has been known how to achieve the bend minimum without any restriction of the size of the vertices. Naturally, the vertices should be represented by uniformly small squares. In addition we might require that each face should be represented by a non-empty region. This would allow a labeling of the faces. We present an efficient algorithm which provably achieves the bend minimum following these constraints. Omitting the latter requirement we conjecture that the problem becomes NP-hard. For that case we give advices for good approximations. We demonstrate the effectiveness of our approaches giving some interesting examples.

2-Visibility Drawings of Planar Graphs

In a 2-visibility drawing the vertices of a given graph are represented by rectangular boxes and the adjacency relations are expressed by horizontal and vertical lines drawn between the boxes. In this paper we want to emphasize this model as a practical alternative to other representations of graphs, and to demonstrate the quality of the produced drawings. We give several approaches, heuristics as well as provably good algorithms, to represent planar graphs within this model. To this, we present a polynomial time algorithm to compute a bend-minimum orthogonal drawing under the restriction that the number of bends at each edge is at most 1.

Algorithms and Area Bounds for Nonplanar Orthogonal Drawings

We report on some extensions of the Kandinsky model: A new and highly nontrivial technique to incorporate nonplanar drawings into the Kandinsky model in the same way as in the GIOTTO approach is presented. This means a major step towards the practical usability of our approach. The used technique even gives new insights for the solvability of network flow problems. Another variant of Kandinsky ensures a minimal size of the vertices removing the requirement of uniform size of each vertex. We present a new technique to evaluate our approach with respect to the area and the number of bends, and to perform a reasonable comparison with the GIOTTO approach.

Nice Drawings for Planar Bipartite Graphs

Graph drawing algorithms usually attempt to display the characteristic properties of the input graphs. In this paper we consider the class of planar bipartite graphs and try to achieve planar drawings such that the bipartiteness property is cleary shown. To this aim, we develop several models, give efficient algorithms to find a corresponding drawing if possible or prove the hardness of the problem.

On Improving Orthogonal Drawings: The 4M-Algorithm

Orthogonal drawings of graphs are widely investigated in the literature and many algorithms have been presented to compute such drawings. Most of these algorithms lead to unpleasant drawings with many bends and a large area. We present methods how to improve the quality of given orthogonal drawings. Our algorithms try to simulate the thinking of a human spectator in order to achieve good results. We also give instructions how to implement the strategies in a way that a good runtime performance can be achieved.

Solving Rectilinear Steiner Tree Problems Exactly in Theory and Practice

The rectilinear Steiner tree problem asks for a shortest tree connecting given points in the plane with rectilinear distance. The best theoretically analyzed algorithm for this problem with a fairly practical behaviour bases on dynamic programming and has a running time of O(n2·.2.62n) (Ganley/Cohoon). The best implementation can solve random problems of size 35 (Salowe/Warme) within a day. In this paper we improve the theoretical worst-case time bound to O(n · 2.38n), for random problem instances we prove a running time of less than O(2n). In practice, our ideas lead to even more drastic improvements. Extensive experiments show that the range for the size of random problems solvable within a day on a workstation is almost doubled. For exponential time algorithms, this is an enormous step.

Approaching the 5/4-Approximation for Rectilinear Steiner Trees

The rectilinear Steiner tree problem requires to find a shortest tree connecting a given set of terminal points in the plane with rectilinear distance. We show that the performance ratios of Zelikovskys[17] heuristic is between 1.3 and 1.3125 (before it was only bounded from above by 1.375), while the performance ratio of the heuristic of Berman and Ramaiyer[1] is at most 1.271 (while the previous bound was 1.347). Moreover, we provide O(n · log2n)-time algorithms that satisfy these performance ratios.

Interactive Orthogonal Graph Drawing: Algorithms and Bounds

Incremental graph drawing is a model gaining more and more importance in many applications. We present algorithms that allow insertions of new vertices into an existing drawing without changing the position of the objects drawn so far. We prove bounds for the quality of our drawings and considerably improve on previous bounds. Here the number of bends and the used area are our quality measures. Besides we discuss lower bounds for this problem.

Visualization of Parallel Execution Graphs

Measuring and evaluating the runtime of parallel programs is a difficult task. In this paper we present tools for performance evaluation and visualization in the distributed thread system (DTS), a programming environment for portable parallel applications. We describe the visualization of a parallel trace log as an execution graph using a novel layout algorithm which has been tailored to expose the structure of multithreaded applications.

Graph visualization API library for application builders

Founded in 1991, Tom Sawyer Software produces quality graph-based architectures for application developers. These technologies include graph management, graph layout, graph diagramming, and graph visualization technologies. This software is growing in scope both architecturally and functionally and is packaged as flexible and well-documented library technology that enables universities, governments, and companies to produce graph drawing applications very quickly and with high quality.