3,668 research outputs found
Maximizing the Total Resolution of Graphs
A major factor affecting the readability of a graph drawing is its
resolution. In the graph drawing literature, the resolution of a drawing is
either measured based on the angles formed by consecutive edges incident to a
common node (angular resolution) or by the angles formed at edge crossings
(crossing resolution). In this paper, we evaluate both by introducing the
notion of "total resolution", that is, the minimum of the angular and crossing
resolution. To the best of our knowledge, this is the first time where the
problem of maximizing the total resolution of a drawing is studied.
The main contribution of the paper consists of drawings of asymptotically
optimal total resolution for complete graphs (circular drawings) and for
complete bipartite graphs (2-layered drawings). In addition, we present and
experimentally evaluate a force-directed based algorithm that constructs
drawings of large total resolution
Stress-Minimizing Orthogonal Layout of Data Flow Diagrams with Ports
We present a fundamentally different approach to orthogonal layout of data
flow diagrams with ports. This is based on extending constrained stress
majorization to cater for ports and flow layout. Because we are minimizing
stress we are able to better display global structure, as measured by several
criteria such as stress, edge-length variance, and aspect ratio. Compared to
the layered approach, our layouts tend to exhibit symmetries, and eliminate
inter-layer whitespace, making the diagrams more compact
Edge Routing with Ordered Bundles
Edge bundling reduces the visual clutter in a drawing of a graph by uniting
the edges into bundles. We propose a method of edge bundling drawing each edge
of a bundle separately as in metro-maps and call our method ordered bundles. To
produce aesthetically looking edge routes it minimizes a cost function on the
edges. The cost function depends on the ink, required to draw the edges, the
edge lengths, widths and separations. The cost also penalizes for too many
edges passing through narrow channels by using the constrained Delaunay
triangulation. The method avoids unnecessary edge-node and edge-edge crossings.
To draw edges with the minimal number of crossings and separately within the
same bundle we develop an efficient algorithm solving a variant of the
metro-line crossing minimization problem. In general, the method creates clear
and smooth edge routes giving an overview of the global graph structure, while
still drawing each edge separately and thus enabling local analysis
Planar Drawings of Fixed-Mobile Bigraphs
A fixed-mobile bigraph G is a bipartite graph such that the vertices of one
partition set are given with fixed positions in the plane and the mobile
vertices of the other part, together with the edges, must be added to the
drawing. We assume that G is planar and study the problem of finding, for a
given k >= 0, a planar poly-line drawing of G with at most k bends per edge. In
the most general case, we show NP-hardness. For k=0 and under additional
constraints on the positions of the fixed or mobile vertices, we either prove
that the problem is polynomial-time solvable or prove that it belongs to NP.
Finally, we present a polynomial-time testing algorithm for a certain type of
"layered" 1-bend drawings
Layered Drawing of Undirected Graphs with Generalized Port Constraints
The aim of this research is a practical method to draw cable plans of complex
machines. Such plans consist of electronic components and cables connecting
specific ports of the components. Since the machines are configured for each
client individually, cable plans need to be drawn automatically. The drawings
must be well readable so that technicians can use them to debug the machines.
In order to model plug sockets, we introduce port groups; within a group, ports
can change their position (which we use to improve the aesthetics of the
layout), but together the ports of a group must form a contiguous block.
We approach the problem of drawing such cable plans by extending the
well-known Sugiyama framework such that it incorporates ports and port groups.
Since the framework assumes directed graphs, we propose several ways to orient
the edges of the given undirected graph. We compare these methods
experimentally, both on real-world data and synthetic data that carefully
simulates real-world data. We measure the aesthetics of the resulting drawings
by counting bends and crossings. Using these metrics, we compare our approach
to Kieler [JVLC 2014], a library for drawing graphs in the presence of port
constraints.Comment: Appears in the Proceedings of the 28th International Symposium on
Graph Drawing and Network Visualization (GD 2020
Preserving Order during Crossing Minimization in Sugiyama Layouts
The Sugiyama algorithm, also known as the layered algorithm or hierarchical algorithm, is an established algorithm to produce crossing-minimal drawings of graphs. It does not, however, consider an initial order of the vertices and edges. We show how ordering real vertices, dummy vertices, and edge ports before crossing minimization may preserve the initial order given by the graph without compromising, on average, the quality of the drawing regarding edge crossings. Even for solutions in which the initial graph order produces more crossings than necessary or the vertex and edge order is conflicting, the proposed approach can produce better crossing-minimal drawings than the traditional approach
Straightening out planar poly-line drawings
We show that any -monotone poly-line drawing can be straightened out while
maintaining -coordinates and height. The width may increase much, but we
also show that on some graphs exponential width is required if we do not want
to increase the height. Likewise -monotonicity is required: there are
poly-line drawings (not -monotone) that cannot be straightened out while
maintaining the height. We give some applications of our result.Comment: The main result turns out to be known (Pach & Toth, J. Graph Theory
2004, http://onlinelibrary.wiley.com/doi/10.1002/jgt.10168/pdf
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