All-Pairs Nearest Neighbors In A Mobile Environment

We present external memory data structures to solve the all-pairs nearest neighbor problem in the setting of points that move with constant velocity. We assume the points move with constant velocity along a line, and the queries we consider are the of the following form: given it time instant t(q), find, for each object y, the object or objects that are closest to y at the time t(q). Also we assume that objects can change their motion at any time.