12,261 research outputs found
Drawing Graphs within Restricted Area
We study the problem of selecting a maximum-weight subgraph of a given graph
such that the subgraph can be drawn within a prescribed drawing area subject to
given non-uniform vertex sizes. We develop and analyze heuristics both for the
general (undirected) case and for the use case of (directed) calculation graphs
which are used to analyze the typical mistakes that high school students make
when transforming mathematical expressions in the process of calculating, for
example, sums of fractions
Transforming planar graph drawings while maintaining height
There are numerous styles of planar graph drawings, notably straight-line
drawings, poly-line drawings, orthogonal graph drawings and visibility
representations. In this note, we show that many of these drawings can be
transformed from one style to another without changing the height of the
drawing. We then give some applications of these transformations
The unknown Oldowan. ~1.7-million-year-old standardized obsidian small tools from Garba IV, Melka Kunture, Ethiopia
The Oldowan Industrial Complex has long been thought to have been static, with limited
internal variability, embracing techno-complexes essentially focused on small-to-medium
flake production. The flakes were rarely modified by retouch to produce small tools, which
do not show any standardized pattern. Usually, the manufacture of small standardized tools
has been interpreted as a more complex behavior emerging with the Acheulean technology.
Here we report on the ~1.7 Ma Oldowan assemblages from Garba IVE-F at Melka Kunture
in the Ethiopian highland. This industry is structured by technical criteria shared by the other
East African Oldowan assemblages. However, there is also evidence of a specific technical
process never recorded before, i.e. the systematic production of standardized small pointed
tools strictly linked to the obsidian exploitation. Standardization and raw material selection
in the manufacture of small tools disappear at Melka Kunture during the Lower Pleistocene
Acheulean. This proves that 1) the emergence of a certain degree of standardization in toolkits
does not reflect in itself a major step in cultural evolution; and that 2) the Oldowan knappers,
when driven by functional needs and supported by a highly suitable raw material,
were occasionally able to develop specific technical solutions. The small tool production at
~1.7 Ma, at a time when the Acheulean was already emerging elsewhere in East Africa,
adds to the growing amount of evidence of Oldowan techno-economic variability and flexibility,
further challenging the view that early stone knapping was static over hundreds of
thousands of years
3D Shape Reconstruction from Sketches via Multi-view Convolutional Networks
We propose a method for reconstructing 3D shapes from 2D sketches in the form
of line drawings. Our method takes as input a single sketch, or multiple
sketches, and outputs a dense point cloud representing a 3D reconstruction of
the input sketch(es). The point cloud is then converted into a polygon mesh. At
the heart of our method lies a deep, encoder-decoder network. The encoder
converts the sketch into a compact representation encoding shape information.
The decoder converts this representation into depth and normal maps capturing
the underlying surface from several output viewpoints. The multi-view maps are
then consolidated into a 3D point cloud by solving an optimization problem that
fuses depth and normals across all viewpoints. Based on our experiments,
compared to other methods, such as volumetric networks, our architecture offers
several advantages, including more faithful reconstruction, higher output
surface resolution, better preservation of topology and shape structure.Comment: 3DV 2017 (oral
On Upward Drawings of Trees on a Given Grid
Computing a minimum-area planar straight-line drawing of a graph is known to
be NP-hard for planar graphs, even when restricted to outerplanar graphs.
However, the complexity question is open for trees. Only a few hardness results
are known for straight-line drawings of trees under various restrictions such
as edge length or slope constraints. On the other hand, there exist
polynomial-time algorithms for computing minimum-width (resp., minimum-height)
upward drawings of trees, where the height (resp., width) is unbounded.
In this paper we take a major step in understanding the complexity of the
area minimization problem for strictly-upward drawings of trees, which is one
of the most common styles for drawing rooted trees. We prove that given a
rooted tree and a grid, it is NP-hard to decide whether
admits a strictly-upward (unordered) drawing in the given grid.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Improved Bounds for Drawing Trees on Fixed Points with L-shaped Edges
Let be an -node tree of maximum degree 4, and let be a set of
points in the plane with no two points on the same horizontal or vertical line.
It is an open question whether always has a planar drawing on such that
each edge is drawn as an orthogonal path with one bend (an "L-shaped" edge). By
giving new methods for drawing trees, we improve the bounds on the size of the
point set for which such drawings are possible to: for
maximum degree 4 trees; for maximum degree 3 (binary) trees; and
for perfect binary trees.
Drawing ordered trees with L-shaped edges is harder---we give an example that
cannot be done and a bound of points for L-shaped drawings of
ordered caterpillars, which contrasts with the known linear bound for unordered
caterpillars.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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