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

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

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

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

Octilinear Force-Directed Layout with Mental Map Preservation for Schematic Diagrams

We present an algorithm for automatically laying out metro map style schematics using a force-directed approach, where we use a localized version of the standard spring embedder forces combined with an octilinear magnetic force. The two types of forces used during layout are naturally conflicting, and the existing method of simply combining these to generate a resultant force does not give satisfactory results. Hence we vary the forces, emphasizing the standard forces in the beginning to produce a well distributed graph, with the octilinear forces becoming prevalent at the end of the layout, to ensure that the key requirement of line angles at intervals of 45? is obtained. Our method is considerably faster than the more commonly used search-based approaches, and we believe the results are superior to the previous force-directed approach. We have further developed this technique to address the issues of dynamic schematic layout. We use a Delaunay triangulation to construct a schematic “frame”, which is used to retain relative node positions and permits full control of the level of mental map preservation. This technique is the first to combine mental map preservation techniques with the additional layout criteria of schematic diagrams. To conclude, we present the results of a study to investigate the relationship between the level of mental map preservation and the user response time and accuracy

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

Incremental Grid-like Layout Using Soft and Hard Constraints

We explore various techniques to incorporate grid-like layout conventions into a force-directed, constraint-based graph layout framework. In doing so we are able to provide high-quality layout---with predominantly axis-aligned edges---that is more flexible than previous grid-like layout methods and which can capture layout conventions in notations such as SBGN (Systems Biology Graphical Notation). Furthermore, the layout is easily able to respect user-defined constraints and adapt to interaction in online systems and diagram editors such as Dunnart.Comment: Accepted to Graph Drawing 201

An automatic generation of metro-like maps to display flight routes for air traffic controllers: structure and color optimization

International audienceAircraft must follow strict Air Traffic Control (ATC) rules. One of these rules is that aircraft have to fly over pre-defined Flight Routes (FR). Current ATC visualizations do not display FRs because they are numerous and run into each other, and thus spoil the visualization. The schematic views for metro maps are used to maximize the transmission of relevant information (lines, metro stops) of network visualization. In this paper, we will focus on two different issues. First, we show how we transposed mathematical constraints used to produce metro maps into the specific field of ATC. The view produced is a context compatible, 2D picture of a schematic maps view for Air Traffic Control. Second, we propose to investigate the generation and placement of colors to be assigned to lines of the network. The first step is to find as many colors as lines of the network. These colors must be perceptually as distinct as possible, and available in the vocabulary of colors. The second step is to solve the NP-complete problem of the optimal assignment of these colors so that close lines have the most perceptively distant color. Finally, we assess the map produced through experimentation to validate its quality

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 ($45^\circ$) line-segments. In this paper, we study octilinear drawings of low edge complexity, i.e., with few bends per edge. A $k$-planar graph is a planar graph in which each vertex has degree less or equal to $k$. 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 $O(n^2) \times O(n)$. 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