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Calculating aggregation operators of moving point objects, using time as a continuous variable, presents unique problems when querying for congestion in a moving and changing (or dynamic) query space. We present a set of congestion query operators, based on a threshold value, that estimate the following 5 aggregation operations in d-dimensions. 1) We call the count of point objects that intersect the dynamic query space during the query time interval, the CountRange. 2) We call the Maximum (or Minimum) congestion in the dynamic query space at any time during the query time interval, the MaxCount (or MinCount). 3) We call the sum of time that the dynamic query space is congested, the ThresholdSum. 4) We call the number of times that the dynamic query space is congested, the ThresholdCount. And 5) we call the average length of time of all the time intervals when the dynamic query space is congested, the ThresholdAverage. These operators rely on a novel approach to transforming the problem of selection based on position to a problem of selection based on a threshold. These operators can be used to predict concentrations of migrating birds that may carry disease such as Bird Flu and hence the information may be used to predict high risk areas. On a smaller scale, those operators are also applicable to maintaining safety in airplane operations. We present the theory of our estimation operators and provide algorithms for exact operators. The implementations of those operators, and experiments, which include data from more than 7500 queries, indicate that our estimation operators produce fast, efficient results with error under 5%., Comment: Technical report on spatiotemporal aggregation prior to journal submission

We describe two efficient on-line algorithms to simplify weighted graphs by eliminating degree-two vertices. Our algorithms are on-line in that they react to updates on the data, keeping the simplification up-to-date. The supported updates are insertions of vertices and edges; hence, our algorithms are partially dynamic. We provide both analytical and empirical evaluations of the efficiency of our approaches. Specifically, we prove an O(log n) upper bound on the amortized time complexity of our maintenance algorithms, with n the number of insertions., Comment: This is the full techreport corresponding to the paper "On-line maintenance of simplified weighted graphs for efficient distance queries" in the proceedings of ACM-GIS 2006

We present a data model for spatio-temporal databases. In this model spatio-temporal data is represented as a finite union of objects described by means of a spatial reference object, a temporal object and a geometric transformation function that determines the change or movement of the reference object in time. We define a number of practically relevant classes of spatio-temporal objects, and give complete results concerning closure under Boolean set operators for these classes. Since only few classes are closed under all set operators, we suggest an extension of the model, which leads to better closure properties, and therefore increased practical applicability. We also discuss a normal form for this extended data model., Comment: 27 pages, 4 figures