Towards Data-Driven Multilinear Metro Maps

Traditionally, most schematic metro maps in practice as well as metro map layout algorithms adhere to an octolinear layout style with all paths composed of horizontal, vertical, and 45{\deg}-diagonal edges. Despite growing interest in more general multilinear metro maps, generic algorithms to draw metro maps based on a system of $k \ge 2$ not necessarily equidistant slopes have not been investigated thoroughly. In this paper we present and implement an adaptation of the octolinear mixed-integer linear programming approach of N\"ollenburg and Wolff (2011) that can draw metro maps schematized to any set C of arbitrary orientations. We further present a data-driven approach to determine a suitable set C by either detecting the best rotation of an equidistant orientation system or by clustering the input edge orientations using a k-means algorithm. We demonstrate the new possibilities of our method using several real-world examples.