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Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming
May 2011 (vol. 17 no. 5)
pp. 626-641
ASCII Text
x 
 
Martin Nöllenburg, Alexander Wolff, "Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 5, pp. 626-641, May, 2011.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2010.81,
author = {Martin Nöllenburg and Alexander Wolff},
title = {Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {17},
number = {5},
issn = {1077-2626},
year = {2011},
pages = {626-641},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2010.81},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Visualization and Computer Graphics
TI - Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming
IS - 5
SN - 1077-2626
SP626
EP641
EPD - 626-641
A1 - Martin Nöllenburg,
A1 - Alexander Wolff,
PY - 2011
KW - Network visualization
KW - graph drawing
KW - graph labeling
KW - metro map
KW - octilinear layout
KW - mixed-integer programming.
VL - 17
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
Martin Nöllenburg, Karlsruhe Institute of Technology (KIT) , Karlsruhe
Alexander Wolff, Universität Würzburg, Würzburg
Metro maps are schematic diagrams of public transport networks that serve as visual aids for route planning and navigation tasks. It is a challenging problem in network visualization to automatically draw appealing metro maps. There are two aspects to this problem that depend on each other: the layout problem of finding station and link coordinates and the labeling problem of placing nonoverlapping station labels. In this paper, we present a new integral approach that solves the combined layout and labeling problem (each of which, independently, is known to be NP-hard) using mixed-integer programming (MIP). We identify seven design rules used in most real-world metro maps. We split these rules into hard and soft constraints and translate them into an MIP model. Our MIP formulation finds a metro map that satisfies all hard constraints (if such a drawing exists) and minimizes a weighted sum of costs that correspond to the soft constraints. We have implemented the MIP model and present a case study and the results of an expert assessment to evaluate the performance of our approach in comparison to both manually designed official maps and results of previous layout methods.

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Index Terms:
Network visualization, graph drawing, graph labeling, metro map, octilinear layout, mixed-integer programming.
Citation:
Martin Nöllenburg, Alexander Wolff, "Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 5, pp. 626-641, May 2011, doi:10.1109/TVCG.2010.81
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