You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
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.

Cited Abstract(s):
[1]: 

[2]: The automatic layout of metro maps has been investigated quite intensely over the last few years. Previous work has focused on the octilinear drawing style where edges are drawn horizontally, vertically, or diagonally at 45°. Inspired by manually created curvy metro maps, we advocate the use of the curvilinear drawing style; we draw edges as Bezier curves. Since we forbid metro lines to bend (even in stations), the user of such a map can trace the metro lines easily. In order to create such drawings, we use the force-directed framework. Our method is the first that directly represents and operates on edges as curves.

[3]: We investigate the new problem of automatic metro map layout. In general, a metro map consists of a set of lines which have intersections or overlaps. We define a set of aesthetic criteria for good metro map layouts and present a method to produce such layouts automatically. Our method uses a variation of the spring algorithm with a suitable preprocessing step. The experimental results with real world data sets show that our method produces good metro map layouts quickly.
Another line of research focuses on drawing metro maps, for example, by restricting the representation of transit lines to octilinear polylines [3] or B 'ezier Curves [2] . See also [1] for a recent survey on automated metro map layout methods. These approaches strongly abstract from the geographical course of the lines (and often also from station positions), and the minimization of line crossings or separations is not part of the problem. In particular, the resulting maps cannot be used for tiles or overlays in typical map services.