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Segmenting trajectories: A framework and algorithms using spatiotemporal criteria

ones we considered, but specific for the purpose. This needs to be done in close collaboration with domain experts and is a topic for further research. Acknowledgments Maike Buchin is supported by the

Four Soviets Walk the Dog: Improved Bounds for Computing the Fréchet Distance

Given two polygonal curves in the plane, there are many ways to define a notion of similarity between them. One popular measure is the Fréchet distance. Since it was proposed by Alt and Godau in 1992, many variants and extensions have been studied. Nonetheless, even more than 20 years later, the original \(O(n^2 \log n)\) algorithm by Alt and Godau for computing the Fréchet...

Computing the Fréchet Distance with a Retractable Leash

All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values. We present a novel approach that avoids the detour through the decision version. This gives the first quadratic time algorithm for the Fréchet...

Similarity of trajectories taking into account geographic context

The movements of animals, people, and vehicles are embedded in a geographic context. This context influences the movement and may cause the formation of certain behavioral responses. Thus, it is essential to include context parameters in the study of movement and the development of movement pattern analytics. Advances in sensor technologies and positioning devices provide...

Median Trajectories

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...

Processing aggregated data: the location of clusters in health data

focus on geographic applications. Maike Buchin received her Ph.D in computer science from the Free University Berlin in Germany. She was a postdoctoral researcher at Utrecht University, Netherlands, and

Drawing (Complete) Binary Tanglegrams

A binary tanglegram is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example, in phylogenetics, it is essential that both trees are drawn without edge crossings and that the inter-tree edges have as few crossings as possible. It is known that finding a...

Polychromatic Colorings of Plane Graphs

We show that the vertices of any plane graph in which every face is incident to at least g vertices can be colored by ⌊(3g−5)/4⌋ colors so that every color appears in every face. This is nearly tight, as there are plane graphs where all faces are incident to at least g vertices and that admit no vertex coloring of this type with more than ⌊(3g+1)/4⌋ colors. We further show that...