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- David Eppstein, Marc J. van Kreveld, Bettina Speckmann, Frank Staals
- Int. J. Comput. Geometry Appl.
- 2013

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 tra-jectories 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… (More)

- Irina Kostitsyna, Marc J. van Kreveld, Maarten Löffler, Bettina Speckmann, Frank Staals
- Symposium on Computational Geometry
- 2015

In recent years trajectory data has become one of the main types of geographic data, and hence algorithmic tools to handle large quantities of trajectories are essential. A single trajectory is typically represented as a sequence of time-stamped points in the plane. In a collection of trajectories one wants to detect maximal groups of moving entities and… (More)

- Arthur van Goethem, Marc J. van Kreveld, Maarten Löffler, Bettina Speckmann, Frank Staals
- Symposium on Computational Geometry
- 2016

We present algorithms and data structures that support the interactive analysis of the grouping structure of one-, two-, or higher-dimensional time-varying data while varying all defining parameters. Grouping structures characterise important patterns in the temporal evaluation of sets of time-varying data. We follow Buchin et al. [9] who define groups… (More)

- Peter Eades, Meng-Wei Chang, +50 authors Daniel Weiskopf
- 2013

- Marc J. van Kreveld, Maarten Löffler, Frank Staals, Lionov Wiratma
- ISAAC
- 2016

One of the important tasks in the analysis of spatio-temporal data collected from moving entities is to find a group: a set of entities that travel together for a sufficiently long period of time. Buchin et al. [2] introduce a formal definition of groups, analyze its mathematical structure, and present efficient algorithms for computing all maximal groups… (More)

- Joachim Gudmundsson, Marc J. van Kreveld, Frank Staals
- SIGSPATIAL/GIS
- 2013

We study one of the basic tasks in moving object analysis, namely the location of <i>hotspots</i>. A hotspot is a (small) region in which an entity spends a significant amount of time. Finding such regions is useful in many applications, for example in segmentation, clustering, and locating popular places. We may be interested in locating a minimum size… (More)

- Ferran Hurtado, Maarten Löffler, +4 authors Frank Staals
- ISAAC
- 2013

We study the problem of visibility in polyhedral terrains in the presence of multiple viewpoints. We consider a triangulated terrain with m > 1 viewpoints (or guards) located on the terrain surface. A point on the terrain is considered visible if it has an unobstructed line of sight to at least one viewpoint. We study several natural and fundamental… (More)

- Boris Aronov, Anne Driemel, Marc J. van Kreveld, Maarten Löffler, Frank Staals
- ACM Trans. Algorithms
- 2015

In the trajectory segmentation problem, we are given a polygonal trajectory with <i>n</i> vertices that we have to subdivide into a minimum number of disjoint segments (subtrajectories) that all satisfy a given criterion. The problem is known to be solvable efficiently for <i>monotone</i> criteria: criteria with the property that if they hold on a certain… (More)