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The existing literature gives efficient algorithms for mapping trees or less restrictively outerplanar graphs on a given set of points in a plane, so that the edges are drawn planar and as straight lines. We relax the latter requirement and allow very few bends on each edge while considering general plane graphs. Our results show two algorithms for mapping… (More)

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 respect to the size of the vertices. Naturally, the vertices should be represented by uniformly small squares. In… (More)

In this paper, we present boundary labeling, a new approach for labeling point sets with large labels. We first place disjoint labels around an axis-parallel rectangle that contains the points. Then we connect each label to its point such that no two connections intersect. Such an approach is common e.g. in technical drawings and medical atlases, but so far… (More)

In this paper, we present algorithms to produce orthogonal drawings of arbitrary graphs. As opposed to most known algorithms, we do not restrict ourselves to graphs with maximum degree 4. The best previous result gave an (m ? 1) (m 2 + 1)-grid for graphs with n nodes and m edges. We present algorithms for two scenarios. In the static scenario, the graph is… (More)

Bipartite graphs are common in many complex systems as they describe a relationship between two different kinds of actors, e.g., genes and proteins, metabolites and enzymes, authors and articles, or products and consumers. A common approach to analyze them is to build a graph between the nodes on one side depending on their relationships with nodes on the… (More)

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.… (More)

In this paper we present a paradigm for solving external-memory problems, and illustrate it by algorithms for matrix multiplication, sorting, list ranking, transitive closure and FFT. Our paradigm is based on the use of BSP algorithms. The correspondence is almost perfect, and especially the notion of x-optimality carries over to algorithms designed… (More)

We consider the problem of routing and sorting on d-dimensional n: : :n mesh connected computers. Each of the processing units initially holds k packets. We present randomized algorithms that solve these problems with (1+o(1))maxf2dn;kn=2g communication steps. On a torus these problems are solved twice as fast. Thus we match the bisection bound up to… (More)

Two trees with the same number of leaves have to be embedded in two layers in the plane such that the leaves are aligned in two adjacent layers. Additional matching edges between the leaves give a one-to-one correspondence between pairs of leaves of the different trees. Do there exist two planar embeddings of the two trees that minimize the crossings of the… (More)