Towards Data-Driven Multilinear Metro Maps

Abstract: 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.