Fast Algorithms for a Class of Temporal Range Queries

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Abstract

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.

Supported in part by the National Science Foundation through the National Partnership for Advanced Computational Infrastructure (NPACI), DoD-MD Procurement under contract MDA90402C0428, and NASA under the ESIP Program NCC5300.