An Algorithmic Framework for Labeling Network Maps

TL;DR

This paper introduces a flexible labeling model for metro maps, proves its computational complexity, and provides an efficient optimal algorithm for single-line labeling, culminating in a practical workflow for multiple lines.

Contribution

It presents a new labeling model for network maps, proves NP-completeness, and offers an optimal algorithm for single-line labeling within a comprehensive workflow.

Findings

NP-completeness of the labeling problem for a single line

Efficient optimal algorithm for restricted single-line labeling

Successful experimental evaluation on real-world metro maps

Abstract

Drawing network maps automatically comprises two challenging steps, namely laying out the map and placing non-overlapping labels. In this paper we tackle the problem of labeling an already existing network map considering the application of metro maps. We present a flexible and versatile labeling model. Despite its simplicity, we prove that it is NP-complete to label a single line of the network. For a restricted variant of that model, we then introduce an efficient algorithm that optimally labels a single line with respect to a given weighting function. Based on that algorithm, we present a general and sophisticated workflow for multiple metro lines, which is experimentally evaluated on real-world metro maps.