19,499 research outputs found
Automatic Metro Map Layout Using Multicriteria Optimization
This paper describes an automatic mechanism for drawing metro maps. We apply multicriteria optimization to find effective placement of stations with a good line layout and to label the map unambiguously. A number of metrics are defined, which are used in a weighted sum to find a fitness value for a layout of the map. A hill climbing optimizer is used to reduce the fitness value, and find improved map layouts. To avoid local minima, we apply clustering techniques to the map the hill climber moves both stations and clusters when finding improved layouts. We show the method applied to a number of metro maps, and describe an empirical study that provides some quantitative evidence that automatically-drawn metro maps can help users to find routes more efficiently than either published maps or undistorted maps. Moreover, we found that, in these cases, study subjects indicate a preference for automatically-drawn maps over the alternatives
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
Improving Search-Based Schematic Layout by Parameter Manipulation
This paper reports on a method to improve the automated layout of schematic diagrams
by widening the search space examined by the system. In search-based layout methods
there are typically a number of parameters that control the search algorithm which do
not affect the fitness function, but nevertheless have an impact on the final layout. We
explore how varying three parameters (grid spacing, the starting distance of allowed
node movement and the number of iterations) affects the resultant diagram in a hill-
climbing layout system. Using an iterative process, we produce diagram layouts that are
significantly better than those produced by ad-hoc parameter settings
Gesture-Based Input for Drawing Schematics on a Mobile Device
We present a system for drawing metro map style schematics using a gesture-based interface. This work brings together techniques in gesture recognition on touch-sensitive devices with research in schematic layout of networks. The software allows users to create and edit schematic networks, and provides an automated layout method for improving the appearance of the schematic. A case study using the metro map metaphor to visualize social networks and web site structure is described
Efficient Generation of Geographically Accurate Transit Maps
We present LOOM (Line-Ordering Optimized Maps), a fully automatic generator
of geographically accurate transit maps. The input to LOOM is data about the
lines of a given transit network, namely for each line, the sequence of
stations it serves and the geographical course the vehicles of this line take.
We parse this data from GTFS, the prevailing standard for public transit data.
LOOM proceeds in three stages: (1) construct a so-called line graph, where
edges correspond to segments of the network with the same set of lines
following the same course; (2) construct an ILP that yields a line ordering for
each edge which minimizes the total number of line crossings and line
separations; (3) based on the line graph and the ILP solution, draw the map. As
a naive ILP formulation is too demanding, we derive a new custom-tailored
formulation which requires significantly fewer constraints. Furthermore, we
present engineering techniques which use structural properties of the line
graph to further reduce the ILP size. For the subway network of New York, we
can reduce the number of constraints from 229,000 in the naive ILP formulation
to about 4,500 with our techniques, enabling solution times of less than a
second. Since our maps respect the geography of the transit network, they can
be used for tiles and overlays in typical map services. Previous research work
either did not take the geographical course of the lines into account, or was
concerned with schematic maps without optimizing line crossings or line
separations.Comment: 7 page
Exploring Local Optima in Schematic Layout
In search-based graph drawing methods there are
typically a number of parameters that control the search algorithm.
These parameters do not affect the ?tness function, but
nevertheless have an impact on the ?nal layout. One such search
method is hill climbing, and, in the context of schematic layout, we
explore how varying three parameters (grid spacing, the starting
distance of allowed node movement and the number of iterations)
affects the resultant diagram. Although we cannot characterize
schematics completely and so cannot yet automatically assign
parameters for diagrams, we observe that when parameters are
set to values that increase the search space, they also tend to
improve the ?nal layout. We come to the conclusion that hillclimbing
methods for schematic layout are more prone to reaching
local optima than had previously been expected and that a wider
search, as described in this paper, can mitigate this, so resulting
in a better layout
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
A Tabu Search Based Approach for Graph Layout
This paper describes an automated tabu search based method for drawing general graph layouts with straight lines. To our knowledge, this is the first time tabu methods have been applied to graph drawing. We formulated the task as a multi-criteria optimization problem with a number of
metrics which are used in a weighted fitness function to measure the aesthetic
quality of the graph layout. The main goal of this work is to speed up the graph
layout process without sacrificing layout quality. To achieve this, we use a tabu
search based method that goes through a predefined number of iterations to minimize
the value of the fitness function. Tabu search always chooses the best solution in
the neighbourhood. This may lead to cycling, so a tabu list is used to store moves
that are not permitted, meaning that the algorithm does not choose previous
solutions for a set period of time. We evaluate the method according to the time
spent to draw a graph and the quality of the drawn graphs. We give experimental
results applied on random graphs and we provide statistical evidence that our
method outperforms a fast search-based drawing method (hill climbing) in execution
time while it produces comparably good graph layouts.We also demonstrate the method
on real world graph datasets to show that we can reproduce similar results in a
real world setting
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
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