546 research outputs found
An Algorithmic Framework for Labeling Network Maps
Drawing network maps automatically comprises two challenging steps, namely
laying out the map and placing non-overlapping labels. In this paper we tackle
the problem of labeling an already existing network map considering the
application of metro maps. We present a flexible and versatile labeling model.
Despite its simplicity, we prove that it is NP-complete to label a single line
of the network. For a restricted variant of that model, we then introduce an
efficient algorithm that optimally labels a single line with respect to a given
weighting function. Based on that algorithm, we present a general and
sophisticated workflow for multiple metro lines, which is experimentally
evaluated on real-world metro maps.Comment: Full version of COCOON 2015 pape
Snapping Graph Drawings to the Grid Optimally
In geographic information systems and in the production of digital maps for
small devices with restricted computational resources one often wants to round
coordinates to a rougher grid. This removes unnecessary detail and reduces
space consumption as well as computation time. This process is called snapping
to the grid and has been investigated thoroughly from a computational-geometry
perspective. In this paper we investigate the same problem for given drawings
of planar graphs under the restriction that their combinatorial embedding must
be kept and edges are drawn straight-line. We show that the problem is NP-hard
for several objectives and provide an integer linear programming formulation.
Given a plane graph G and a positive integer w, our ILP can also be used to
draw G straight-line on a grid of width w and minimum height (if possible).Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
MetroSets: Visualizing Sets as Metro Maps
We propose MetroSets, a new, flexible online tool for visualizing set systems
using the metro map metaphor. We model a given set system as a hypergraph
, consisting of a set of vertices and a set
, which contains subsets of called hyperedges. Our system then
computes a metro map representation of , where each hyperedge
in corresponds to a metro line and each vertex corresponds to a
metro station. Vertices that appear in two or more hyperedges are drawn as
interchanges in the metro map, connecting the different sets. MetroSets is
based on a modular 4-step pipeline which constructs and optimizes a path-based
hypergraph support, which is then drawn and schematized using metro map layout
algorithms. We propose and implement multiple algorithms for each step of the
MetroSet pipeline and provide a functional prototype with \new{easy-to-use
preset configurations.} % many real-world datasets. Furthermore, \new{using
several real-world datasets}, we perform an extensive quantitative evaluation
of the impact of different pipeline stages on desirable properties of the
generated maps, such as octolinearity, monotonicity, and edge uniformity.Comment: 19 pages; accepted for IEEE INFOVIS 2020; for associated live system,
see http://metrosets.ac.tuwien.ac.a
Drawing metro maps in concentric circles: A designerâinâtheâloop approach with visual examples
This article presents a proof-of-concept designer-in-the-loop schematic map drawing tool, based on the marriage of two approachesâmanual and automated, which provides the technical interactivity of drawing tools between the user and the computer. We focus on concentric circle maps as opposed to the commonly used orthogonal mode representation, which is suggested by previous studies that it could promote better network learning. In comparison with existing methods, the proposed method is more compatible with the framework of effective map design from psychological and aesthetic perspectives, and a range of options can be provided in conjunction with users' preferences. We evaluated our approach on a set of iterations with case studies of Hong Kong metro with a group of three co-authors from the fields of geography, transport engineering, and education
Automated drawing of metro maps
This work investigates the problem of drawing metro maps which is defined as follows. Given a planar graph G of maximum degree 8 with its embedding and vertex locations (e.g. the physical location of the tracks and stations of a metro system) and a set L of paths or cycles in G (e.g. metro lines) such that each edge of G belongs to at least one element of L, draw G and L nicely. We first specify the niceness of a drawing by listing a number of hard and soft constraints. Then we show that it is NP-complete to decide whether a drawing of G satisfying all hard constraints exists. In spite of the hardness of the problem we present a mixed-integer linear program (MIP) which always finds a drawing that fulfills all hard constraints (if such a drawing exists) and optimizes a weighted sum of costs corresponding to the soft constraints. We also describe some heuristics that speed up the MIP and we show how to include vertex labels in the drawing. We have implemented the MIP, the heuristics and the vertex labeling. For six real-world examples we compare our results to official metro maps drawn by graphic designers and to the results of previous algorithms for drawing metro maps
Planar Octilinear Drawings with One Bend Per Edge
In octilinear drawings of planar graphs, every edge is drawn as an
alternating sequence of horizontal, vertical and diagonal ()
line-segments. In this paper, we study octilinear drawings of low edge
complexity, i.e., with few bends per edge. A -planar graph is a planar graph
in which each vertex has degree less or equal to . In particular, we prove
that every 4-planar graph admits a planar octilinear drawing with at most one
bend per edge on an integer grid of size . For 5-planar
graphs, we prove that one bend per edge still suffices in order to construct
planar octilinear drawings, but in super-polynomial area. However, for 6-planar
graphs we give a class of graphs whose planar octilinear drawings require at
least two bends per edge
What?s your theory of effective schematic map design?
Amongst designers, researchers, and the general public, there exists a diverse array of opinion about good practice in schematic map design, and a lack of awareness that such opinions are not necessarily universally held nor supported by evidence. This paper gives an overview of the range of opinion that can be encountered, the consequences that this has for published designs, and a framework for organising the various views
- âŠ