Validity Information Retrieval for Spatio-Temporal Queries: Theoretical Performance Bounds

The results of traditional spatial queries (i.e., range search, nearest neighbor, etc.) are usually meaningless in spatio-temporal applications, because they will be invalidated by the movements of query and/or data objects. In practice, a query result R should be accompanied with validity information specifying (i) the (future) time T that R will expire, and (ii) the change C of R at time T (so that R can be updated incrementally). Although several algorithms have been proposed for this problem, their worst-case performance is the same as that of sequential scan. This paper presents the first theoretical study on validity queries, and develops indexes and algorithms with attractive I/O complexities. Our discussion covers numerous important variations of the problem and different query/object mobility combinations. The solutions involve a set of nontrivial reductions that reveal the problem characteristics and permit the deployment of existing structures. 1 Problem Formulation Traditional spatial query processing is insufficient in spatio-temporal applications, where the data and/or query objects change their locations. Consider, for example, a moving user who asks for the nearest hotel; the result (e.g., hotel a) of a conventional nearest neighbor query is by itself meaningless because it may be invalidated as soon as the user moves. In practice, the query result R should be accompanied by additional validity information: (i) the expiry time T of R, i.e., the future time when a ceases to be the nearest hotel (based on the user’s moving direction and speed), and (ii) the result change C at T (e.g., the next nearest hotel after a expires). This problem is not specific to nearest neighbor search, but actually exists in all query types [TP02]. In this paper, we discuss validity information retrieval for the most common spatial queries, namely, (orthogonal) range search (RS) and nearest neighbor (NN) queries, considering oneor twodimensional objects with linear movements. Following the common modeling in the literature [SJLL00, GBE+00], a moving point p is represented using its location p(0) at the system reference time 0, and its current velocity v (p(0) and v are 1D/2D vectors), such that its location p(t) at any future time t can be This is the Pre-Published Version