A new framework for addressing temporal range queries and some preliminary results

Given a set of n objects each characterized by d attributes speci ed at m xed time instances we are interested in the problem of designing space e cient indexing structures such that arbitrary temporal range search queries can be handled e ciently When m our problem reduces to the d dimensional orthogonal search problem We establish e cient 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 logm log log n f for one sided queries when d where f is the number of objects satisfying the query A similar result is shown for counting queries We also show that the most general problem can be solved with a polylogarithmic query time using nonlinear space data structures