1,023 research outputs found
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
New Approaches to Classic Graph-Embedding Problems - Orthogonal Drawings & Constrained Planarity
Drawings of graphs are often used to represent a given data set in a human-readable way. In this thesis, we consider different classic algorithmic problems that arise when automatically generating graph drawings. More specifically, we solve some open problems in the context of orthogonal drawings and advance the current state of research on the problems clustered planarity and simultaneous planarity
A generic design concept for geometric algorithms
The design phase of an algorithm’s implementation is confronted with the
issues of efficiency, flexibility, and ease-of-use. In this paper, we suggest
a concept that greatly increases the flexibility of an implementation without
sacrificing its ease-of-use. The loss in terms of efficiency is small. We
demonstrate the advantages of our concept at a C++ implementation of a simple
rectangleintersection algorithm, which follows the well-known sweep-line
paradigm. We lead the reader from a naive interface in a step-by-step guide to
an interface offering full flexibility. The gain in flexibility can reduce
implementation effort by facilitating code reusage. Reusability in turn helps
to achieve correctness since more users mean more testing. Though most of the
ingredients of our concept have already been suggested elsewhere, to our
knowledge this is the first time that they are applied vigorously in a
geometric setting. We include a thorough experimental analysis on random and
real world data that arouse in the context of map labeling
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