Fast algorithms for a class of temporal range queries

Given a set of n objects, each characterized by d attributes specified at m fixed time instances, we are interested in the problem of designing efficient indexing structures such that the following type of queries can be handled efficiently: given d value ranges and a time interval, report or count all the objects whose attributes fall within the corresponding d value ranges at each time instance lying in the specified time interval. We establish efficient data structures to handle several classes of the general problem. Our results include a linear size data structure that enables a query time of O(log n log m + f) for one-sided queries when d=1, where f is the output size. We also show that the most general problem can be solved with polylogarithmic query time using nonlinear space data structures.