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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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We present LOOM (Line-Ordering Optimized Maps), a fully automatic generator of geographically accurate transit maps. The input to LOOM is data about the lines of a given transit network, namely for each line, the sequence of stations it serves and the geographical course the vehicles of this line take. We parse this data from GTFS, the prevailing standard for public transit data. LOOM proceeds in three stages: (1) construct a so-called line graph, where edges correspond to segments of the network with the same set of lines following the same course; (2) construct an ILP that yields a line ordering for each edge which minimizes the total number of line crossings and line separations; (3) based on the line graph and the ILP solution, draw the map. As a naive ILP formulation is too demanding, we derive a new custom-tailored formulation which requires significantly fewer constraints. Furthermore, we present engineering techniques which use structural properties of the line graph to further reduce the ILP size. For the subway network of New York, we can reduce the number of constraints from 229,000 in the naive ILP formulation to about 4,500 with our techniques, enabling solution times of less than a second. Since our maps respect the geography of the transit network, they can be used for tiles and overlays in typical map services. Previous research work either did not take the geographical course of the lines into account, or was concerned with schematic maps without optimizing line crossings or line separations.

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