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

Schematic bus transit maps for the web using genetic algorithms

Dissertation submitted in partial fulfilment of the requirements for the degree of Master of Science in Geospatial TechnologiesThe octilinear schematic map, layout recognized worldwide in metro maps, is an important transit informative tool. This research investigates how algorithms for the visualization of schematic maps can be availed in mobile web devices context in order to empower the efficiency in transmitting information of bus transit maps. A genetic algorithm for path octilinear schematization technique has been used and tested to create the schematic data. Location-based and interactivity functionalities were embedded to the resulting digital maps in order to create personalized maps to meet specific user needs. A prototype of a web application and real transit data of the city of Castellón in Spain was used to test the methodology. The results have shown that real time schematizations open possibilities concerning usability that add extra value to schematic transit maps. Additionally, suggested improvements have been made to the genetic algorithm and performance tests show that genetic algorithms are adequate, in terms of efficiency, to sketch bus transit maps automatically

On d-regular Schematization of Embedded Paths

In the d-regular path schematization problem we are given an embedded path P (e.g.,a route in a road network) and an integer d. The goal is to find a d-schematized embedding of P in which the orthogonal order of allvertices in the input is preserved and in which every edge has a slope that is an integer multiple of 90/d. We show that deciding whether a path can be d-schematized is NP-hard for any integer d. We further model the problem as a mixed-integer linear program. An experimental evaluation indicates that this approach generates reasonable route sketches for real-world data

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

Visualization Algorithms for Maps and Diagrams

One of the most common visualization tools used by mankind are maps or diagrams. In this thesis we explore new algorithms for visualizing maps (road and argument maps). A map without any textual information or pictograms is often without use so we research also further into the field of labeling maps. In particular we consider the new challenges posed by interactive maps offered by mobile devices. We discuss new algorithmic approaches and experimentally evaluate them

Schematization of Road Networks

We study the problem of computing schematized versions of network maps, like railroad maps. Every path of the schematized map has two or three links with restricted orientations, and topologically, the schematized map must be equivalent to the input map. Our approach applies to several types of schematizations, and certain additional constraints can be added. In the general case our algorithm takes O(n log 3 n) time, and when all paths in the input are monotone in some (not necessarily the same) direction, it runs in O(n log n) time. 1