85 research outputs found
An Interactive Tool to Explore and Improve the Ply Number of Drawings
Given a straight-line drawing of a graph , for every vertex
the ply disk is defined as a disk centered at where the radius of
the disk is half the length of the longest edge incident to . The ply number
of a given drawing is defined as the maximum number of overlapping disks at
some point in . Here we present a tool to explore and evaluate
the ply number for graphs with instant visual feedback for the user. We
evaluate our methods in comparison to an existing ply computation by De Luca et
al. [WALCOM'17]. We are able to reduce the computation time from seconds to
milliseconds for given drawings and thereby contribute to further research on
the ply topic by providing an efficient tool to examine graphs extensively by
user interaction as well as some automatic features to reduce the ply number.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
A Distributed Multilevel Force-directed Algorithm
The wide availability of powerful and inexpensive cloud computing services
naturally motivates the study of distributed graph layout algorithms, able to
scale to very large graphs. Nowadays, to process Big Data, companies are
increasingly relying on PaaS infrastructures rather than buying and maintaining
complex and expensive hardware. So far, only a few examples of basic
force-directed algorithms that work in a distributed environment have been
described. Instead, the design of a distributed multilevel force-directed
algorithm is a much more challenging task, not yet addressed. We present the
first multilevel force-directed algorithm based on a distributed vertex-centric
paradigm, and its implementation on Giraph, a popular platform for distributed
graph algorithms. Experiments show the effectiveness and the scalability of the
approach. Using an inexpensive cloud computing service of Amazon, we draw
graphs with ten million edges in about 60 minutes.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Placing Arrows in Directed Graph Drawings
We consider the problem of placing arrow heads in directed graph drawings
without them overlapping other drawn objects. This gives drawings where edge
directions can be deduced unambiguously. We show hardness of the problem,
present exact and heuristic algorithms, and report on a practical study.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
A Sparse Stress Model
Force-directed layout methods constitute the most common approach to draw
general graphs. Among them, stress minimization produces layouts of
comparatively high quality but also imposes comparatively high computational
demands. We propose a speed-up method based on the aggregation of terms in the
objective function. It is akin to aggregate repulsion from far-away nodes
during spring embedding but transfers the idea from the layout space into a
preprocessing phase. An initial experimental study informs a method to select
representatives, and subsequent more extensive experiments indicate that our
method yields better approximations of minimum-stress layouts in less time than
related methods.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Modularity clustering is force-directed layout
Two natural and widely used representations for the community structure of
networks are clusterings, which partition the vertex set into disjoint subsets,
and layouts, which assign the vertices to positions in a metric space. This
paper unifies prominent characterizations of layout quality and clustering
quality, by showing that energy models of pairwise attraction and repulsion
subsume Newman and Girvan's modularity measure. Layouts with optimal energy are
relaxations of, and are thus consistent with, clusterings with optimal
modularity, which is of practical relevance because both representations are
complementary and often used together.Comment: 9 pages, 7 figures, see http://code.google.com/p/linloglayout/ for
downloading the graph clustering and layout softwar
Application of Approximate Pattern Matching in Two Dimensional Spaces to Grid Layout for Biochemical Network Maps
Background
For visualizing large-scale biochemical network maps, it is important to calculate the coordinates of molecular nodes quickly and to enhance the understanding or traceability of them. The grid layout is effective in drawing compact, orderly, balanced network maps with node label spaces, but existing grid layout algorithms often require a high computational cost because they have to consider complicated positional constraints through the entire optimization process.
Results
We propose a hybrid grid layout algorithm that consists of a non-grid, fast layout (preprocessor) algorithm and an approximate pattern matching algorithm that distributes the resultant preprocessed nodes on square grid points. To demonstrate the feasibility of the hybrid layout algorithm, it is characterized in terms of the calculation time, numbers of edge-edge and node-edge crossings, relative edge lengths, and F-measures. The proposed algorithm achieves outstanding performances compared with other existing grid layouts.
Conclusions
Use of an approximate pattern matching algorithm quickly redistributes the laid-out nodes by fast, non-grid algorithms on the square grid points, while preserving the topological relationships among the nodes. The proposed algorithm is a novel use of the pattern matching, thereby providing a breakthrough for grid layout. This application program can be freely downloaded from http://www.cadlive.jp/hybridlayout/hybridlayout.html
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