Anne Driemel

Approximating the Fréchet Distance for Realistic Curves in Near Linear Time

We present a simple and practical (1+ε)-approximation algorithm for the Fréchet distance between two polygonal curves in ℝd. To analyze this algorithm we introduce a new realistic family of curves, c-packed curves, that is closed under simplification. We believe the notion of c-packed curves to be of independent interest. We show that our algorithm has near linear running time for c-packed polygonal curves, and similar results for other input models, such as low-density polygonal curves.

An algorithmic framework for segmenting trajectories based on spatio-temporal criteria

In this paper we address the problem of segmenting a trajectory such that each segment is in some sense homogeneous. We formally define different spatio-temporal criteria under which a trajectory can be homogeneous, including location, heading, speed, velocity, curvature, sinuosity, and curviness. We present a framework that allows us to segment any trajectory into a minimum number of segments under any of these criteria, or any combination of these criteria. In this framework, the segmentation problem can generally be solved in O(n log n) time, where n is the number of edges of the trajectory to be segmented.

Jaywalking your dog: Computing the fréchet distance with shortcuts

The similarity of two polygonal curves can be measured using the Frechet distance. We introduce the notion of a more robust Frechet distance, where one is allowed to shortcut between vertices of one of the curves. This is a natural approach for handling noise, in particular batched outliers. We compute a

Approximating the Fréchet distance for realistic curves in near linear time

(3+\varepsilon)

Computing the Fréchet distance with shortcuts is NP-hard

-approximation to the minimum Frechet distance over all possible such shortcuts, in near linear time, if the curve is

Computing the Fréchet distance between folded polygons

c

Segmentation of Trajectories on Nonmonotone Criteria

-packed and the number of shortcuts is either small or unbounded. To facilitate the new algorithm we develop several new tools: (a) a data structure for preprocessing a curve (not necessarily

Locality-sensitive hashing of curves

c

On the Expected Complexity of Voronoi Diagrams on Terrains

-packed) that supports

Approximate map matching with respect to the Fréchet distance

(1+\varepsilon)