47,836 research outputs found
Achieving Good Angular Resolution in 3D Arc Diagrams
We study a three-dimensional analogue to the well-known graph visualization
approach known as arc diagrams. We provide several algorithms that achieve good
angular resolution for 3D arc diagrams, even for cases when the arcs must
project to a given 2D straight-line drawing of the input graph. Our methods
make use of various graph coloring algorithms, including an algorithm for a new
coloring problem, which we call localized edge coloring.Comment: 12 pages, 5 figures; to appear at the 21st International Symposium on
Graph Drawing (GD 2013
Optimal 3D Angular Resolution for Low-Degree Graphs
We show that every graph of maximum degree three can be drawn in three
dimensions with at most two bends per edge, and with 120-degree angles between
any two edge segments meeting at a vertex or a bend. We show that every graph
of maximum degree four can be drawn in three dimensions with at most three
bends per edge, and with 109.5-degree angles, i.e., the angular resolution of
the diamond lattice, between any two edge segments meeting at a vertex or bend.Comment: 18 pages, 10 figures. Extended version of paper to appear in Proc.
18th Int. Symp. Graph Drawing, Konstanz, Germany, 201
Lombardi Drawings of Graphs
We introduce the notion of Lombardi graph drawings, named after the American
abstract artist Mark Lombardi. In these drawings, edges are represented as
circular arcs rather than as line segments or polylines, and the vertices have
perfect angular resolution: the edges are equally spaced around each vertex. We
describe algorithms for finding Lombardi drawings of regular graphs, graphs of
bounded degeneracy, and certain families of planar graphs.Comment: Expanded version of paper appearing in the 18th International
Symposium on Graph Drawing (GD 2010). 13 pages, 7 figure
Maximizing the Total Resolution of Graphs
A major factor affecting the readability of a graph drawing is its
resolution. In the graph drawing literature, the resolution of a drawing is
either measured based on the angles formed by consecutive edges incident to a
common node (angular resolution) or by the angles formed at edge crossings
(crossing resolution). In this paper, we evaluate both by introducing the
notion of "total resolution", that is, the minimum of the angular and crossing
resolution. To the best of our knowledge, this is the first time where the
problem of maximizing the total resolution of a drawing is studied.
The main contribution of the paper consists of drawings of asymptotically
optimal total resolution for complete graphs (circular drawings) and for
complete bipartite graphs (2-layered drawings). In addition, we present and
experimentally evaluate a force-directed based algorithm that constructs
drawings of large total resolution
Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity
We describe a linear-time algorithm that finds a planar drawing of every
graph of a simple line or pseudoline arrangement within a grid of area
O(n^{7/6}). No known input causes our algorithm to use area
\Omega(n^{1+\epsilon}) for any \epsilon>0; finding such an input would
represent significant progress on the famous k-set problem from discrete
geometry. Drawing line arrangement graphs is the main task in the Planarity
puzzle.Comment: 12 pages, 8 figures. To appear at 21st Int. Symp. Graph Drawing,
Bordeaux, 201
Proximity Drawings of High-Degree Trees
A drawing of a given (abstract) tree that is a minimum spanning tree of the
vertex set is considered aesthetically pleasing. However, such a drawing can
only exist if the tree has maximum degree at most 6. What can be said for trees
of higher degree? We approach this question by supposing that a partition or
covering of the tree by subtrees of bounded degree is given. Then we show that
if the partition or covering satisfies some natural properties, then there is a
drawing of the entire tree such that each of the given subtrees is drawn as a
minimum spanning tree of its vertex set
- …