7,591 research outputs found
A graph rewriting programming language for graph drawing
This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally complete languages which give a visual view of graphs both whilst programming and during execution. Grrr, based on the Spider system, is a general purpose graph rewriting programming language which has now been extended in order to demonstrate the feasibility of visual graph drawing
Orthogonal Graph Drawing with Inflexible Edges
We consider the problem of creating plane orthogonal drawings of 4-planar
graphs (planar graphs with maximum degree 4) with constraints on the number of
bends per edge. More precisely, we have a flexibility function assigning to
each edge a natural number , its flexibility. The problem
FlexDraw asks whether there exists an orthogonal drawing such that each edge
has at most bends. It is known that FlexDraw is NP-hard
if for every edge . On the other hand, FlexDraw can
be solved efficiently if and is trivial if
for every edge .
To close the gap between the NP-hardness for and the
efficient algorithm for , we investigate the
computational complexity of FlexDraw in case only few edges are inflexible
(i.e., have flexibility~). We show that for any FlexDraw
is NP-complete for instances with inflexible edges with
pairwise distance (including the case where they
induce a matching). On the other hand, we give an FPT-algorithm with running
time , where
is the time necessary to compute a maximum flow in a planar flow network with
multiple sources and sinks, and is the number of inflexible edges having at
least one endpoint of degree 4.Comment: 23 pages, 5 figure
Graph-Drawing Contest Report
This report describes the Sixth Annual Graph Drawing Contest, held in conjunction with the 1999 Graph Drawing Symposium in Prague, Czech Republic. The purpose of the contest is to monitor and challenge the current state of the art in graph-drawing technology
The Galois Complexity of Graph Drawing: Why Numerical Solutions are Ubiquitous for Force-Directed, Spectral, and Circle Packing Drawings
Many well-known graph drawing techniques, including force directed drawings,
spectral graph layouts, multidimensional scaling, and circle packings, have
algebraic formulations. However, practical methods for producing such drawings
ubiquitously use iterative numerical approximations rather than constructing
and then solving algebraic expressions representing their exact solutions. To
explain this phenomenon, we use Galois theory to show that many variants of
these problems have solutions that cannot be expressed by nested radicals or
nested roots of low-degree polynomials. Hence, such solutions cannot be
computed exactly even in extended computational models that include such
operations.Comment: Graph Drawing 201
05191 Abstracts Collection -- Graph Drawing
From 08.05.05 to 13.05.05, the Dagstuhl Seminar 05191 ``Graph Drawing\u27\u27 was held
in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Choosing Colors for Geometric Graphs via Color Space Embeddings
Graph drawing research traditionally focuses on producing geometric
embeddings of graphs satisfying various aesthetic constraints. After the
geometric embedding is specified, there is an additional step that is often
overlooked or ignored: assigning display colors to the graph's vertices. We
study the additional aesthetic criterion of assigning distinct colors to
vertices of a geometric graph so that the colors assigned to adjacent vertices
are as different from one another as possible. We formulate this as a problem
involving perceptual metrics in color space and we develop algorithms for
solving this problem by embedding the graph in color space. We also present an
application of this work to a distributed load-balancing visualization problem.Comment: 12 pages, 4 figures. To appear at 14th Int. Symp. Graph Drawing, 200
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