New Results on Trajectory Grouping under Geodesic Distance ∗

We study grouping of entities moving amidst obstacles, extending the recent work of Kostitsyna et al. [5]. We present an alternative algorithm that can compute the Reeb-graph, a graph which captures when and how the partition of the entities into groups changes, when the entities move amidst arbitrary polygonal obstacles. Our new algorithm is significantly faster than the algorithm of Kostitsyna et al. when the number of entities is significantly larger than the total complexity of the obstacles. Furthermore, we consider a restricted setting in which the obstacles are big compared to ε: the parameter determining when entities are close enough together to be in the same group. We show that in this setting the Reeb-graph is much smaller, and we can compute it much faster, than in the case of general obstacles.