On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
The complexity of the free space for a robot moving amidst fat obstacles
Computational Geometry: Theory and Applications
Computing minimum length paths of a given homotopy class
Computational Geometry: Theory and Applications
Trajectory clustering with mixtures of regression models
KDD '99 Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining
Taking a Walk in a Planar Arrangement
SIAM Journal on Computing
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Trajectory clustering: a partition-and-group framework
Proceedings of the 2007 ACM SIGMOD international conference on Management of data
TraClass: trajectory classification using hierarchical region-based and trajectory-based clustering
Proceedings of the VLDB Endowment
Detecting Commuting Patterns by Clustering Subtrajectories
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
The projection median of a set of points
Computational Geometry: Theory and Applications
The frechet distance revisited and extended
Proceedings of the twenty-seventh annual symposium on Computational geometry
Median trajectories using well-visited regions and shortest paths
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Measuring similarity between curves on 2-manifolds via homotopy area
Proceedings of the twenty-ninth annual symposium on Computational geometry
The fréchet distance revisited and extended
ACM Transactions on Algorithms (TALG)
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We investigate the concept of a median among a set of trajectories. We establish criteria that a "median trajectory" should meet, and present two different methods to construct a median for a set of input trajectories. The first method is very simple, while the second method is more complicated and uses homotopy with respect to sufficiently large faces in the arrangement formed by the trajectories. We give algorithms for both methods, analyze the worst-case running time, and show that under certain assumptions both methods can be implemented efficiently. We empirically compare the output of both methods on randomly generated trajectories, and analyze whether the two methods yield medians that are according to our intuition. Our results suggest that the second method, using homotopy, performs considerably better.