# Automated drawing of metro maps

@inproceedings{Nllenburg2005AutomatedDO, title={Automated drawing of metro maps}, author={Martin N{\"o}llenburg}, year={2005} }

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…

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## 23 Citations

An ILP for the metro-line crossing problem

- Mathematics, Computer ScienceCATS
- 2008

It is proved that the problem, which is known to be NP-hard, can be rewritten as an integer linear program that finds the optimal solution for the problem in polynomial time.

Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming

- Computer ScienceIEEE Transactions on Visualization and Computer Graphics
- 2011

This paper identifies seven design rules used in most real-world metro maps and translates them into an MIP model, which finds a metro map that satisfies all hard constraints and minimizes a weighted sum of costs that correspond to the soft constraints.

Drawing Metro Maps on Concentric Circles

- Computer Science
- 2016

This thesis examines algorithms for the drawing of metro maps by adapting the Topology-ShapeMetrics framework by Roberto Tamassia to create a drawing in which the lines bend as little as possible and shows that achieving an optimal compaction is also NP-hard.

Snapping Graph Drawings to the Grid Optimally

- MathematicsGraph Drawing
- 2016

It is shown that the problem is NP-hard for several objectives and an integer linear programming formulation is provided that can be used to draw G straight-line on a grid of width w and minimum height (if possible).

On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings

- MathematicsAlgorithmica
- 2018

An algorithm is presented that produces bi-monotone smooth orthogonal drawings with at most two segments per edge, which also guarantees a linear number of edges with exactly one segment.

A Survey on Automated Metro Map Layout Methods

- Computer Science
- 2012

This survey distinguishes three subtasks of generating metro map layouts (schematic network layout, label placement, crossing minimization) and gives a list of ten design rules that form the basis of the layout algorithms.

Automatic Metro Map Layout Using Multicriteria Optimization

- Computer ScienceIEEE Transactions on Visualization and Computer Graphics
- 2011

An empirical study is described 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.

A survey of direction-preserving layout strategies

- Computer ScienceSCCG
- 2014

Different layout algorithms that preserve relative directions in geo-referenced networks, an important criterion for many sensor networks such as the electric grid and other supply networks, are analyzed.

On d-Regular Schematization of Embedded Paths

- Mathematics, Computer ScienceSOFSEM
- 2011

It is shown that deciding whether a path can be d-schematized is NP-hard for any integer d and that this approach generates reasonable route sketches for real-world data.

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