Efficient aggregation over moving objects

We study two types of aggregation queries over a set S moving point objects. The first asks to count the number of points in S that are dominated by a query point Q at a given time t. The second asks to find the maximum number of points in S that are dominated by a query point at any time. These queries have several applications in the area of Geographic Information Systems and spatiotemporal databases. For the first query and any fixed dimension d, we give two different solutions, one using O (√ N) time and O (N) space and another using O (log N) time and O (N² space, where N is the number of moving points. When each of the points in S is moving piecewise linearly along the same line and the total number of pieces is O (N), then we can do the count query in O (√ N) time and O (N) space. For the second query, when all objects move along the x-axis, we give a solution that uses O (log N) time and O (N²) space in the worst case. Our solutions introduce novel search structures that can have other applications.