Metro Maps on Octilinear Grid Graphs

Schematic transit maps (often called “metro maps” in the literature) are important to produce comprehensible visualizations of complex public transit networks. In this work, we investigate the problem of automatically drawing such maps on an octilinear grid with an arbitrary (but optimal) number of...

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Bibliographic Details
Published in:Computer graphics forum Vol. 39; no. 3; pp. 357 - 367
Main Authors: Bast, Hannah, Brosi, Patrick, Storandt, Sabine
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.06.2020
Subjects:
Algorithms
Bends
CCS Concepts
Human‐centered computing → Graph drawings; • Theory of computation → Integer programming; • Mathematics of computing → Approximation algorithms
Mathematical analysis
Optimization
Public transportation
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:Schematic transit maps (often called “metro maps” in the literature) are important to produce comprehensible visualizations of complex public transit networks. In this work, we investigate the problem of automatically drawing such maps on an octilinear grid with an arbitrary (but optimal) number of edge bends. Our approach can naturally deal with obstacles that should be respected in the final drawing (points of interest, rivers, coastlines) and can prefer grid edges near the real‐world course of a line. This allows our drawings to be combined with existing maps, for example as overlays in map services. We formulate an integer linear program which can be used to solve the problem exactly. We also provide a fast approximation algorithm which greedily calculates shortest paths between node candidates on the underlying octilinear grid graph. Previous work used local search techniques to update node positions until a local optimum was found, but without guaranteeing octilinearity. We can thus calculate nearly optimal metro maps in a fraction of a second even for complex networks, enabling the interactive use of our method in map editors.
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13986