9,098 research outputs found
On some special classes of contact -VPG graphs
A graph is a -VPG graph if one can associate a path on a rectangular
grid with each vertex such that two vertices are adjacent if and only if the
corresponding paths intersect at at least one grid-point. A graph is a
contact -VPG graph if it is a -VPG graph admitting a representation
with no two paths crossing and no two paths sharing an edge of the grid. In
this paper, we present a minimal forbidden induced subgraph characterisation of
contact -VPG graphs within four special graph classes: chordal graphs,
tree-cographs, -tidy graphs and -free graphs. Moreover, we present a
polynomial-time algorithm for recognising chordal contact -VPG graphs.Comment: 34 pages, 15 figure
Risk Assessment Algorithms Based On Recursive Neural Networks
The assessment of highly-risky situations at road intersections have been
recently revealed as an important research topic within the context of the
automotive industry. In this paper we shall introduce a novel approach to
compute risk functions by using a combination of a highly non-linear processing
model in conjunction with a powerful information encoding procedure.
Specifically, the elements of information either static or dynamic that appear
in a road intersection scene are encoded by using directed positional acyclic
labeled graphs. The risk assessment problem is then reformulated in terms of an
inductive learning task carried out by a recursive neural network. Recursive
neural networks are connectionist models capable of solving supervised and
non-supervised learning problems represented by directed ordered acyclic
graphs. The potential of this novel approach is demonstrated through well
predefined scenarios. The major difference of our approach compared to others
is expressed by the fact of learning the structure of the risk. Furthermore,
the combination of a rich information encoding procedure with a generalized
model of dynamical recurrent networks permit us, as we shall demonstrate, a
sophisticated processing of information that we believe as being a first step
for building future advanced intersection safety system
Recognizing clique graphs of directed and rooted path graphs
AbstractWe describe characterizations for the classes of clique graphs of directed and rooted path graphs. The characterizations relate these classes to those of clique-Helly and strongly chordal graphs, respectively, which properly contain them. The characterizations lead to polynomial time algorithms for recognizing graphs of these classes
Contact Representations of Graphs in 3D
We study contact representations of graphs in which vertices are represented
by axis-aligned polyhedra in 3D and edges are realized by non-zero area common
boundaries between corresponding polyhedra. We show that for every 3-connected
planar graph, there exists a simultaneous representation of the graph and its
dual with 3D boxes. We give a linear-time algorithm for constructing such a
representation. This result extends the existing primal-dual contact
representations of planar graphs in 2D using circles and triangles. While
contact graphs in 2D directly correspond to planar graphs, we next study
representations of non-planar graphs in 3D. In particular we consider
representations of optimal 1-planar graphs. A graph is 1-planar if there exists
a drawing in the plane where each edge is crossed at most once, and an optimal
n-vertex 1-planar graph has the maximum (4n - 8) number of edges. We describe a
linear-time algorithm for representing optimal 1-planar graphs without
separating 4-cycles with 3D boxes. However, not every optimal 1-planar graph
admits a representation with boxes. Hence, we consider contact representations
with the next simplest axis-aligned 3D object, L-shaped polyhedra. We provide a
quadratic-time algorithm for representing optimal 1-planar graph with L-shaped
polyhedra
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