5,470 research outputs found
Pole Dancing: 3D Morphs for Tree Drawings
We study the question whether a crossing-free 3D morph between two
straight-line drawings of an -vertex tree can be constructed consisting of a
small number of linear morphing steps. We look both at the case in which the
two given drawings are two-dimensional and at the one in which they are
three-dimensional. In the former setting we prove that a crossing-free 3D morph
always exists with steps, while for the latter steps
are always sufficient and sometimes necessary.Comment: Appears in the Proceedings of the 26th International Symposium on
Graph Drawing and Network Visualization (GD 2018
A Universal Point Set for 2-Outerplanar Graphs
A point set is universal for a class if
every graph of has a planar straight-line embedding on . It is
well-known that the integer grid is a quadratic-size universal point set for
planar graphs, while the existence of a sub-quadratic universal point set for
them is one of the most fascinating open problems in Graph Drawing. Motivated
by the fact that outerplanarity is a key property for the existence of small
universal point sets, we study 2-outerplanar graphs and provide for them a
universal point set of size .Comment: 23 pages, 11 figures, conference version at GD 201
The discovery of 12min X-ray pulsations from 1WGA J1958.2+3232
During a systematic search for periodic signals in a sample of ROSAT PSPC
(0.1-2.4 keV) light curves, we discovered 12min large amplitude X-ray
pulsations in 1WGA J1958.2+3232, an X-ray source which lies close to the
galactic plane. The energy spectrum is well fit by a power law with a photon
index of 0.8, corresponding to an X-ray flux of about 10E-12 ergs cmE-2 sE-1.
The source is probably a long period, low luminosity X-ray pulsar, similar to X
Per, or an intermediate polar.Comment: 5 pages (figures included). Accepted for publication on MNRA
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
Euclidean Greedy Drawings of Trees
Greedy embedding (or drawing) is a simple and efficient strategy to route
messages in wireless sensor networks. For each source-destination pair of nodes
s, t in a greedy embedding there is always a neighbor u of s that is closer to
t according to some distance metric. The existence of greedy embeddings in the
Euclidean plane R^2 is known for certain graph classes such as 3-connected
planar graphs. We completely characterize the trees that admit a greedy
embedding in R^2. This answers a question by Angelini et al. (Graph Drawing
2009) and is a further step in characterizing the graphs that admit Euclidean
greedy embeddings.Comment: Expanded version of a paper to appear in the 21st European Symposium
on Algorithms (ESA 2013). 24 pages, 20 figure
Extending Upward Planar Graph Drawings
In this paper we study the computational complexity of the Upward Planarity
Extension problem, which takes in input an upward planar drawing of
a subgraph of a directed graph and asks whether can be
extended to an upward planar drawing of . Our study fits into the line of
research on the extensibility of partial representations, which has recently
become a mainstream in Graph Drawing.
We show the following results.
First, we prove that the Upward Planarity Extension problem is NP-complete,
even if has a prescribed upward embedding, the vertex set of coincides
with the one of , and contains no edge.
Second, we show that the Upward Planarity Extension problem can be solved in
time if is an -vertex upward planar -graph. This
result improves upon a known -time algorithm, which however applies to
all -vertex single-source upward planar graphs.
Finally, we show how to solve in polynomial time a surprisingly difficult
version of the Upward Planarity Extension problem, in which is a directed
path or cycle with a prescribed upward embedding, contains no edges, and no
two vertices share the same -coordinate in
Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition
A geometric graph is angle-monotone if every pair of vertices has a path
between them that---after some rotation---is - and -monotone.
Angle-monotone graphs are -spanners and they are increasing-chord
graphs. Dehkordi, Frati, and Gudmundsson introduced angle-monotone graphs in
2014 and proved that Gabriel triangulations are angle-monotone graphs. We give
a polynomial time algorithm to recognize angle-monotone geometric graphs. We
prove that every point set has a plane geometric graph that is generalized
angle-monotone---specifically, we prove that the half--graph is
generalized angle-monotone. We give a local routing algorithm for Gabriel
triangulations that finds a path from any vertex to any vertex whose
length is within times the Euclidean distance from to .
Finally, we prove some lower bounds and limits on local routing algorithms on
Gabriel triangulations.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Simultaneous Embeddings with Few Bends and Crossings
A simultaneous embedding with fixed edges (SEFE) of two planar graphs and
is a pair of plane drawings of and that coincide when restricted to
the common vertices and edges of and . We show that whenever and
admit a SEFE, they also admit a SEFE in which every edge is a polygonal curve
with few bends and every pair of edges has few crossings. Specifically: (1) if
and are trees then one bend per edge and four crossings per edge pair
suffice (and one bend per edge is sometimes necessary), (2) if is a planar
graph and is a tree then six bends per edge and eight crossings per edge
pair suffice, and (3) if and are planar graphs then six bends per edge
and sixteen crossings per edge pair suffice. Our results improve on a paper by
Grilli et al. (GD'14), which proves that nine bends per edge suffice, and on a
paper by Chan et al. (GD'14), which proves that twenty-four crossings per edge
pair suffice.Comment: Full version of the paper "Simultaneous Embeddings with Few Bends and
Crossings" accepted at GD '1
Probing the Low Mass X-ray Binaries/Globular Cluster connection in NGC1399
We present a wide field study of the Globular Clusters/Low Mass X-ray
Binaries connection in the cD elliptical NGC1399, combining HST/ACS and Chandra
high resolution data. We find evidence that LMXB formation likelihood is
influenced by GCs structural parameters, in addition to the well known effects
of mass and metallicity, independently from galactocentric distance.Comment: in press in the Proceedings of the X-ray 2009 Conference, 7-11
September 2009, Bologna, Ital
Provenance, manufacturing and corrosion behavior of Ancient Hellenistic coins from Egypt
Some copper alloy coins of the Ptolemaic period from a private collection, providing valuable evidence for both archaeometric as well as materials science and corrosion studies, have been investigated. The coins were found in the ancient city of Bubastis, known as Tell Basta, in the Nile Delta, Egypt. The coins have been examined by optical microscopy for their metallurgical structure, analysed by X-ray fluorescence and Electron Dispersion Spectroscopy for their composition, and by X-ray diffraction for the characterisation of their corrosion products. An attempt has been made to remove part of their corrosion products by mild chemical cleaning procedures. In some areas the coins are heavily corroded by chlorides, however most of the inscriptions on the coins themselves are still decipherable. Assumptions are made on the coins provenance, the production period, the manufacturing technique and the burial environmental conditions
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