A predictive spatio-temporal query retrieves the set of moving objects that will intersect a query window during a future time interval. Currently, the only access method for processing such queries in practice is the TPR-tree. In this paper we first perform an analysis to determine the factors that affect the performance of predictive queries and show that several of these factors are not considered by the TPR-tree, which uses the insertion/deletion algorithms of the R*-tree designed for static data. Motivated by this, we propose a new index structure called the TPR*- tree, which takes into account the unique features of dynamic objects through a set of improved construction algorithms. In addition, we provide cost models that determine the optimal performance achievable by any data-partition spatio-temporal access method. Using experimental comparison, we illustrate that the TPR*-tree is nearly-optimal and significantly outperforms the TPR-tree under all conditions.

Spatiotemporal objects, i.e., objects which change their position and/or extent over time appear in many applications. In this paper we examine the problem of indexing large volumes of such data. Important in this environment is how the spatiotemporal objects move and/or change. We consider a rather general case where object movements/changes are defined by combinations of polynomial functions. We further concentrate on "snapshot" as well as small "interval" queries as these are quite common when examining the history of the gathered data. The obvious approach that approximates each spatiotemporal object by an MBR and uses a traditional multidimensional access method to index them is inefficient. Objects that "live" for long time intervals have large MBRs which introduce a lot of empty space. Clustering long intervals has been dealt in temporal databases by the use of partially persistent indices. What differentiates this problem from traditional temporal indexing, is that objects are allowed to move/change during their lifetime. Better ways are thus needed to approximate general spatiotemporal objects. One obvious solution is to introduce artificial splits: the lifetime of a long-lived object is split into smaller consecutive pieces. This decreases the empty space but increases the number of indexed MBRs. We first give an optimal algorithm and a heuristic for splitting a given spatiotemporal object in a predefined number of pieces. Then, given an upper bound on the total number of possible splits, we present three algorithms that decide how the splits are distributed among all the objects so that the total empty space is minimized. The number of splits cannot be increased indefinitely since the extra objects will eventually affect query performance. Usi...

In this thesis, we investigate the subject of indexing large collections of spatiotemporal trajectories for similarity matching. Our proposed technique is to first mitigate the dimensionality curse problem by approximating each trajectory with a low order polynomial-like curve, and then incorporate a multidimensional index into the reduced space of polynomial coefficients. There are many possible ways to choose the polynomial, including Fourier transforms, splines, non-linear regressions, etc. Some of these possibilities have indeed been studied before. We hypothesize that one of the best approaches is the polynomial that minimizes the maximum deviation from the true value, which is called the minimax polynomial. Minimax approximation is particularly meaningful for indexing because in a branch-and-bound search (i.e., for finding nearest neighbours), the smaller the maximum deviation, the more pruning opportunities there exist. In general, among all the polynomials of the same degree, the optimal minimax polynomial is very hard to compute. However, it has been shown that the Chebyshev approximation is almost identical to the optimal minimax polynomial, and is easy to compute [32]. Thus, we shall explore how to use

The rapid increase in spatio-temporal applications calls for new auxiliary indexing structures. A typical spatio-temporal application is one that tracks the behavior of moving objects through location-aware devices (e.g., GPS). Through the last decade, many spatio-temporal access methods are developed. Spatio-temporal access methods focus on two orthogonal directions: (1) Indexing the past, (2) Indexing the current and predicted future positions. In this short survey, we classify spatio-temporal access methods for each direction based on their underlying structure with a brief discussion of future research directions.

With the proliferation of mobile computing, the ability to index efficiently the movements of mobile objects becomes important. Objects are typically seen as moving in two-dimensional (x,y) space, which means that their movements across time may be embedded in the three-dimensional (x,y,t) space. Further, the movements are typically represented as trajectories, sequences of connected line segments. In certain cases, movement is restricted, and specifically in this paper, we aim at exploiting that movements occur in transportation networks to reduce the dimensionality of the data. Briefly, the idea is to reduce movements to occur in one spatial dimension. As a consequence, the movement data becomes two-dimensional (x,t). The advantages of considering such lowerdimensional trajectories are the reduced overall size of the data and the lower-dimensional indexing challenge. Since off-the-shelf database management systems typically do not offer higherdimensional indexing, this reduction in dimensionality allows us to use such DBMSes to store and index trajectories. Moreover, we argue that, given the right circumstances, indexing these dimensionality-reduced trajectories can be more efficient than using a three-dimensional index. This hypothesis is verified by an experimental study that incorporates trajectories stemming from real and synthetic road networks.

Abstract—A range aggregate query returns summarized information about the points falling in a hyper-rectangle (e.g., the total number of these points instead of their concrete ids). This paper studies spatial indexes that solve such queries efficiently and proposes the aggregate Point-tree (aP-tree), which achieves logarithmic cost to the data set cardinality (independently of the query size) for two-dimensional data. The aP-tree requires only small modifications to the popular multiversion structural framework and, thus, can be implemented and applied easily in practice. We also present models that accurately predict the space consumption and query cost of the aP-tree and are therefore suitable for query optimization. Extensive experiments confirm that the proposed methods are efficient and practical. Index Terms—Database, spatial database, range queries, aggregation. 1

Abstract. In this paper, we describe an efficient indexing method for a shape-based similarity search of the trajectory of dynamically changing locations of people and mobile objects. In order to manage trajectories in database systems, we define a data model of trajectories as directed lines in a space, and the similarity between trajectories is defined as the Euclidean distance between directed discrete lines. Our proposed similarity query can be used to find interested patterns embedded into the trajectories, for example, the trajectories of mobile cars in a city may include patterns for expecting traffic jams. Furthermore, we propose an efficient indexing method to retrieve similar trajectories for a query by combining a spatial indexing technique (R +-Tree) and a dimension reduction technique, which is called PAA (Piecewise Approximate Aggregate). The indexing method can efficiently retrieve trajectories whose shape in a space is similar to the shape of a candidate trajectory from the database. 1

With the proliferation of wireless communications and geo-positioning, e-services are envisioned that exploit the positions of a set of continuously moving users to provide context-aware functionality to each individual user. Because advances in disk capacities continue to outperform Moore's Law, it becomes increasingly feasible to store on-line all the position information obtained from the moving e-service users. With the much slower advances in I/O speeds and many concurrent users, indexing techniques are of essence in this scenario. Past

Spatio-temporal objects — that is, objects that evolve over time — appear in many applications. Due to the nature of such applications, storing the evolution of objects through time in order to answer historical queries (queries that refer to past states of the evolution) requires a very large specialized database, what is termed in this article as a spatio-temporal archive. Efficient processing of historical queries on spatio-temporal archives requires equally sophisticated indexing schemes. Typical spatio-temporal indexing techniques represent the objects using minimum bounding regions (MBR) extended with a temporal dimension, which are then indexed using traditional multi-dimensional index structures. However, rough MBR approximations introduce excessive overlap between index nodes which deteriorates query performance. This article introduces a robust indexing scheme for answering spatio-temporal queries more efficiently. A number of algorithms and heuristics are elaborated, which can be used to preprocess a spatiotemporal archive in order to produce finer object approximations which, in combination with a multi-version index structure, will greatly improve query performance in comparison to the straightforward approaches. The proposed techniques introduce a query-efficiency vs. space tradeoff, that can help tune a structure according to available resources. Empirical observations for estimating the necessary amount of additional storage space required for improving query performance by a given factor are also provided. Moreover, heuristics for applying the proposed ideas in an online setting are discussed. Finally, a thorough experimental evaluation is conducted to show the merits of the proposed techniques.

The domain of spatiotemporal applications is a treasure trove of new types of data and queries. In this work, the focus is on a spatiotemporal sub-domain, namely the trajectories of moving point objects. We examine the issues posed by this type of data with respect to indexing and point out existing approaches and research directions. An important aspect of movement is the scenario in which it occurs. Three different scenarios, namely unconstrained movement, constrained movement, and movement in networks are used to categorize various indexing approaches. Each of these scenarios give us different means to either simplify indexing, or to improve the overall query processing performance.