A data structure for dynamic trees
Journal of Computer and System Sciences
Computing longest duration flocks in trajectory data
GIS '06 Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Efficient algorithms for mining maximal valid groups
The VLDB Journal — The International Journal on Very Large Data Bases
Computational Geometry: Theory and Applications
Time-varying Reeb graphs for continuous space--time data
Computational Geometry: Theory and Applications
Modeling Herds and Their Evolvements from Trajectory Data
GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
Discovery of convoys in trajectory databases
Proceedings of the VLDB Endowment
On-line discovery of flock patterns in spatio-temporal data
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Swarm: mining relaxed temporal moving object clusters
Proceedings of the VLDB Endowment
Reeb graphs: approximation and persistence
Proceedings of the twenty-seventh annual symposium on Computational geometry
On discovering moving clusters in spatio-temporal data
SSTD'05 Proceedings of the 9th international conference on Advances in Spatial and Temporal Databases
A deterministic o(m log m) time algorithm for the reeb graph
Proceedings of the twenty-eighth annual symposium on Computational geometry
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The collective motion of a set of moving entities like people, birds, or other animals, is characterized by groups arising, merging, splitting, and ending. Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept from topology. The trajectory grouping structure has three natural parameters, namely group size, group duration, and entity inter-distance. These parameters allow us to obtain detailed or global views of the data. We prove complexity bounds on the maximum number of maximal groups that can be present, and give algorithms to compute the grouping structure efficiently. Furthermore, we showcase the results of experiments using data generated by the NetLogo flocking model and from the Starkey project. Although there is no ground truth for the groups in this data, the experiments show that the trajectory grouping structure is plausible and has the desired effects when changing the essential parameters. Our research provides the first complete study of trajectory group evolvement, including combinatorial, algorithmic, and experimental results.