Joachim Gudmundsson

Computing longest duration flocks in trajectory data

Moving point object data can be analyzed through the discovery of patterns. We consider the computational efficiency of computing two of the most basic spatio-temporal patterns in trajectories, namely flocks and meetings. The patterns are large enough subgroups of the moving point objects that exhibit similar movement and proximity for a certain amount of time. We consider the problem of computing a longest duration flock or meeting. We give several exact and approximation algorithms, and also show that some variants are as hard as MaxClique to compute and approximate.

Efficient detection of motion patterns in spatio-temporal data sets

Moving point object data can be analyzed through the discovery of patterns. We consider the computational efficiency of detecting four such spatio-temporal patterns, namely flock, leadership, convergence, and encounter, as defined by Laube et al., 2004. These patterns are large enough subgroups of the moving point objects that exhibit similar movement in the sense of direction, heading for the same location, and/or proximity. By the use of techniques from computational geometry, including approximation algorithms, we improve the running time bounds of existing algorithms to detect these patterns.

Efficient Detection of Patterns in 2D Trajectories of Moving Points

Moving point object data can be analyzed through the discovery of patterns in trajectories. We consider the computational efficiency of detecting four such spatio-temporal patterns, namely flock, leadership, convergence, and encounter, as defined by Laube et al., Finding REMO—detecting relative motion patterns in geospatial lifelines, 201–214, (2004). These patterns are large enough subgroups of the moving point objects that exhibit similar movement in the sense of direction, heading for the same location, and/or proximity. By the use of techniques from computational geometry, including approximation algorithms, we improve the running time bounds of existing algorithms to detect these patterns.

Reporting Leaders and Followers among Trajectories of Moving Point Objects

Widespread availability of location aware devices (such as GPS receivers) promotes capture of detailed movement trajectories of people, animals, vehicles and other moving objects, opening new options for a better understanding of the processes involved. In this paper we investigate spatio-temporal movement patterns in large tracking data sets. We present a natural definition of the pattern ‘one object is leading others’, which is based on behavioural patterns discussed in the behavioural ecology literature. Such leadership patterns can be characterised by a minimum time length for which they have to exist and by a minimum number of entities involved in the pattern. Furthermore, we distinguish two models (discrete and continuous) of the time axis for which patterns can start and end. For all variants of these leadership patterns, we describe algorithms for their detection, given the trajectories of a group of moving entities. A theoretical analysis as well as experiments show that these algorithms efficiently report leadership patterns.

Constructing plane spanners of bounded degree and low weight

Abstract Given a set S of n points in the plane, we give an O(n log n)-time algorithm that constructs a plane t-spanner for S, with t ≈ 10, such that the degree of each point of S is bounded from above by 27, and the total edge length is proportional to the weight of a minimum spanning tree of S. Previously, no algorithms were known for constructing plane t-spanners of bounded degree.

Fast Greedy Algorithms for Constructing Sparse Geometric Spanners

Given a set V of n points in

TSP with neighborhoods of varying size

\IR^d

Ordered theta graphs

and a real constant t>1, we present the first O(nlog n)-time algorithm to compute a geometric t-spanner on V. A geometric t-spanner on V is a connected graph G = (V,E) with edge weights equal to the Euclidean distances between the endpoints, and with the property that, for all

Constrained free space diagrams: a tool for trajectory analysis

u,v\in V

Approximate distance oracles for geometric graphs

, the distance between u and v in G is at most t times the Euclidean distance between u and v. The spanner output by the algorithm has O(n) edges and weight