Efficient Threshold Aggregation of Moving Objects
  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%. 
Scot Anderson, Peter Revesz