No abstract

The collection of moving object data is becoming more and more common, and therefore there is an increasing need for the efficient analysis and knowledge extraction of these data in different application domains. Trajectory data are normally available as sample points, and do not carry semantic information, which is of fundamental importance for the comprehension of these data. Therefore, the analysis of trajectory data becomes expensive from a computational point of view and complex from a user's perspective. Enriching trajectories with semantic geographical information may simplify queries, analysis, and mining of moving object data. In this paper we propose a data preprocessing model to add semantic information to trajectories in order to facilitate trajectory data analysis in different application domains. The model is generic enough to represent the important parts of trajectories that are relevant to the application, not being restricted to one specific application. We present an algorithm to compute the important parts and show that the query complexity for the semantic analysis of trajectories will be significantly reduced with the proposed model.

No abstract

No abstract

Moving objects produce trajectories. We describe a data model for trajectories and trajectory samples and an efficient way of modeling uncertainty via beads for trajectory samples. We study transformations of the ambient space for which important physical properties of trajectories, such as speed, are invariant. We also determine which transformations preserve beads. We give conceptually easy first-order complete query languages and computationally complete query languages for trajectory databases, which allow to talk directly about speed and uncertainty in terms of beads. The queries expressible in these languages are invariant under speed-and bead-preserving transformations.

We investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.

No abstract

Space-time prisms capture all possible locations of a moving person or object between two known locations and times given the maximum travel velocities in the environment. These known locations or 'anchor points' can represent observed locations or mandatory locations because of scheduling constraints. The classic space-time prism as well as more recent analytical and computational versions in planar space and networks assume that these anchor points are perfectly known or fixed. In reality, observations of anchor points can have error, or the scheduling constraints may have some degree of pliability. This article generalizes the concept of anchor points to anchor regions: these are bounded, possibly disconnected, subsets of space-time containing all possible locations for the anchor points, with each location labelled with an anchor probability. We develop two algorithms for calculating network-based space-time prisms based on these probabilistic anchor regions. The first algorithm calculates the envelope of all space-time prisms having an anchor point within a particular anchor region. The second algorithm calculates, for any space-time point, the probability that a space-time prism with given anchor regions contains that particular point. Both algorithms are implemented in Mathematica to visualize travel possibilities in case the anchor points of a space-time prism are uncertain. We also discuss the complexity of the procedures, their use in analysing uncertainty or flexibility in network-based prisms and future research directions