A Unified Model and Algorithms for Temporal Map Labeling

We consider map labeling for the case that a map undergoes a sequence of operations such as rotation, zoom and translation over a specified time span. We unify and generalize several previous models for dynamic map labeling into one versatile and flexible model. In contrast to previous research, we completely abstract from the particular operations and express the labeling problem as a set of time intervals representing the labels’ presences, activities and conflicts. One of the model’s strength is manifested in its simplicity and broad range of applications. In particular, it supports label selection both for map features with fixed position as well as for moving entities (e.g., for tracking vehicles in logistics or air traffic control). We study the active range maximization problem in this model. We prove that the problem is NP-complete and W[1]-hard, and present constant-factor approximation algorithms. In the restricted, yet practically relevant case that no more than k labels can be active at any time, we give polynomial-time algorithms as well as constant-factor approximation algorithms.