We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t; report all K points of S that lie inside R at time t: We first present an indexing structure that, for any given constant e> 0; uses OðN=BÞ disk blocks and answers a query in OððN=BÞ 1=2þe þ K=BÞ I/Os, where B is the block size. It can also report all the points of S that lie inside R during a given time interval. A point can be inserted or deleted, or the trajectory of a point can be changed, in Oðlog 2 B NÞ I/Os. Next, we present a general approach that improves the query time if the queries arrive in chronological order, by allowing the index to evolve over time. We obtain a tradeoff between the query time and the number of times the index needs to be updated as the points move. We also describe an indexing scheme in which the number of I/Os required to answer a query depends monotonically on the difference between the query time stamp t and the current time. Finally, we develop an efficient indexing scheme to answer approximate

We investigate techniques for analysis and retrieval of object trajectories in a two or three dimensional space. Such kind of data usually contain a great amount of noise, that makes all previously used metrics fail. Therefore, here we formalize non-metric similarity functions based on the Longest Common Subsequence (LCSS), which are very robust to noise and furthermore provide an intuitive notion of similarity between trajectories by giving more weight to the similar portions of the sequences. Stretching of sequences in time is allowed, as well as global translating of the sequences in space. Efficient approximate algorithms that compute these similarity measures are also provided. We compare these new methods to the widely used Euclidean and Time Warping distance functions (for real and synthetic data) and show the superiority of our approach, especially under the strong presence of noise. We prove a weaker version of the triangle inequality and employ it in an indexing structure to answer nearest neighbor queries. Finally, we present experimental results that validate the accuracy and efficiency of our approach. 1

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.

Moving object environments are characterized by large numbers of moving objects and numerous concurrent continuous queries over these objects. Efficient evaluation of these queries in response to the movement of the objects is critical for supporting acceptable response times. In such environments the traditional approach of building an index on the objects (data) suffers from the need for frequent updates and thereby results in poor performance. In fact, a brute force, no-index strategy yields better performance in many cases. Neither the traditional approach, nor the brute force strategy achieve reasonable query processing times. This paper develops novel techniques for the efficient and scalable evaluation of multiple continuous queries on moving objects. Our solution leverages two complimentary techniques: Query Indexing and Velocity Constrained Indexing (VCI). Query Indexing relies on i) incremental evaluation; ii) reversing the role of queries and data; and iii) exploiting the relative locations of objects and queries. VCI takes advantage of the maximum possible speed of objects in order to delay the expensive operation of updating an index to reflect the movement of objects. In contrast to an earlier technique [29] that requires exact knowledge about the movement of the objects, VCI does not rely on such information. While Query Indexing outperforms VCI, it does not efficiently handle the arrival of new queries. Velocity constrained indexing, on the other hand, is unaffected by changes in queries. We demonstrate that a combination of Query Indexing and Velocity Constrained Indexing enables the scalable execution of insertion and deletion of queries in addition to processing ongoing queries. We also develop several optimizations and present a detaile...

A continuous nearest neighbor query retrieves the nearest neighbor (NN) of every point on a line segment (e.g., "find all my nearest gas stations during my route from point s to point e"). The result contains a set of <point, interval> tuples, such that point is the NN of all points in the corresponding interval. Existing methods for continuous nearest neighbor search are based on the repetitive application of simple NN algorithms, which incurs significant overhead. In this paper we propose techniques that solve the problem by performing a single query for the whole input segment. As a result the cost, depending on the query and dataset characteristics, may drop by orders of magnitude.

This paper introduces the Scalable INcremental hash-based Algorithm (SINA, for short); a new algorithm for evaluating a set of concurrent continuous spatio-temporal queries. SINA is designed with two goals in mind: (1) Scalability in terms of the number of concurrent continuous spatiotemporal queries, and (2) Incremental evaluation of continuous spatio-temporal queries. SINA achieves scalability by employing a shared execution paradigm where the execution of continuous spatio-temporal queries is abstracted as a spatial join between a set of moving objects and a set of moving queries. Incremental evaluation is achieved by computing only the updates of the previously reported answer. We introduce two types of updates, namely positive and negative updates. Positive or negative updates indicate that a certain object should be added to or removed from the previously reported answer, respectively. SINA manages the computation of positive and negative updates via three phases: the hashing phase, the invalidation phase, and the joining phase. The hashing phase employs an in-memory hash-based join algorithm that results in a set of positive updates. The invalidation phase is triggered every T seconds or when the memory is fully occupied to produce a set of negative updates. Finally, the joining phase is triggered by the end of the invalidation phase to produce a set of both positive and negative updates that result from joining in-memory data with in-disk data. Experimental results show that SINA is scalable and is more e#cient than other index-based spatio-temporal algorithms.

With the continued proliferation of wireless networks, e.g., based on such evolving standards as WAP and Bluetooth, visionaries predict that the Internet will soon extend to billions of wireless devices, or objects. A substantial fraction of these will offer their changing positions to the (location-based) services, they either use or support. As a result, software technologies that enable the management of the positions of objects capable of continuous movement are in increasingly high demand. This paper assumes what we consider a realistic Internet-service scenario where objects that have not reported their position within a specified duration of time are expected to no longer be interested in, or of interest to, the service. In this scenario, the possibility of substantial quantities of "expiring" objects introduces a new kind of implicit update, which contributes to rendering the database highly dynamic. The paper presents an R-tree based technique for the indexing of the current positions of such objects. Extensive performance experiments explore the properties of the types of bounding regions that are candidates for being used in the internal entries of the index, and they show that, when compared to the approach where the objects are not assumed to expire, the new indexing technique can improve the search performance by as much as a factor of two or more without sacrificing update performance.

It is infeasible for a sensor database to contain the exact value of each sensor at all points in time. This uncertainty is inherent in these systems due to measurement and sampling errors, and resource limitations. In order to avoid drawing erroneous conclusions based upon stale data, the use of uncertainty intervals that model each data item as a range and associated probability density function (pdf) rather than a single value has recently been proposed. Querying these uncertain data introduces imprecision into answers, in the form of probability values that specify the likeliness the answer satisfies the query. These queries are more expensive to evaluate than their traditional counterparts but are guaranteed to be correct and more informative due to the probabilities accompanying the answers. Although the answer probabilities are useful, for many applications, it is only necessary to know whether the probability exceeds a given threshold – we term these Probabilistic Threshold Queries (PTQ). In this paper we address the efficient computation of these types of queries. In particular, we develop two index structures and associated algorithms to efficiently answer PTQs. The first index scheme is based on the idea of augmenting uncertainty information to an R-tree. We establish the difficulty

In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worst-case efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.

We present a general technique for approximating various descriptors of the extent of a set P of n points in R . For a given extent measure and a parameter " > 0, it computes in time O(n + 1=" ) a subset Q P of size 1=" , with the property that (1 ")(P ) (Q) (P ). The speci c applications of our technique include "-approximation algorithms for (i) computing diameter, width, and smallest bounding box, ball, and cylinder of P , (ii) maintaining all the previous measures for a set of moving points, and (iii) tting spheres and cylinders through a point set P . Our algorithms are considerably simpler, and faster in many cases, than the known algorithms.