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

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...

Location monitoring is an important issue for real time management of mobile object positions. Significant research efforts have been dedicated to techniques for efficient processing of spatial continuous queries on moving objects in a centralized location monitoring system. Surprisingly, very few have promoted a distributed approach to real-time location monitoring. In this paper we present a distributed and scalable solution to processing continuously moving queries on moving objects and describe the design of MobiEyes, a distributed real-time location monitoring system in a mobile environment. Mobieyes utilizes the computational power at mobile objects, leading to significant savings in terms of server load and messaging cost when compared to solutions relying on central processing of location information at the server. We introduce a set of optimization techniques, such as Lazy Query Propagation, Query Grouping, and Safe Periods, to constrict the amount of computations handled by the moving objects and to enhance the performance and system utilization of Mobieyes. We also provide a simulation model in a mobile setup to study the scalability of the MobiEyes distributed location monitoring approach with regard to server load, messaging cost, and amount of computation required on the mobile objects.

An important consideration in similarity-based retrieval of moving object trajectories is the definition of a distance function. The existing distance functions are usually sensitive to noise, shifts and scaling of data that commonly occur due to sensor failures, errors in detection techniques, disturbance signals, and different sampling rates. Cleaning data to eliminate these is not always possible. In this paper, we introduce a novel distance function, Edit Distance on Real sequence (EDR) which is robust against these data imperfections. Analysis and comparison of EDR with other popular distance

Advances in hardware-related technologies promise to enable new data management applications that monitor continuous processes. In these applications, enormous amounts of state samples are obtained via sensors and are streamed to a database. Further, updates are very frequent and may exhibit locality. While the R-tree is the index of choice for multi-dimensional data with low dimensionality, and is thus relevant to these applications, R-tree updates are also relatively inefficient.

With the rapid advances of wireless communications and positioning techniques, tracking the positions of moving objects is becoming increasingly feasible and necessary. Traditional spatial index structures are not suitable for storing these positions because of numerous update operations. To reduce the number of update operations, many existing approaches use a linear function to describe the movements of objects. In many real applications, however, the movements of objects are too complicated to be represented as a simple linear function. In this case, such approaches based on a linear function cannot reduce update cost efficiently. In this paper, we propose a novel R-tree based indexing technique called LUR-tree. This technique updates the structure of the index only when an object moves out of the corresponding MBR (minimum bounding rectangle). If a new position of an object is in the MBR, it changes only the position of the object in the leaf node. It can update the position of the object quickly and reduce update cost greatly. Since it is based on the R-tree, the LUR-tree also uses the same algorithms to process various types of queries as the R-tree. We present the experimental results which show that our technique outperforms other techniques 1.

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...

A number of emerging applications of data management technology involve the monitoring and querying of large quantities of continuous variables, e.g., the positions of mobile service users, termed moving objects. In such applications, large quantities of state samples obtained via sensors are streamed to a database. Indexes for moving objects must support queries efficiently, but must also support frequent updates. Indexes based on minimum bounding regions (MBRs) such as the R-tree exhibit high concurrency overheads during node splitting, and each individual update is known to be quite costly. This motivates the design of a solution that enables the B -tree to manage moving objects. We represent moving-object locations as vectors that are timestamped based on their update time. By applying a novel linearization technique to these values, it is possible to index the resulting values using a single B that partitions values according to their timestamp and otherwise preserves spatial proximity. We develop algorithms for range and nearest neighbor queries, as well as continuous queries. The proposal can be grafted into existing database systems cost effectively. An extensive experimental study explores the performance characteristics of the proposal and also shows that it is capable of substantially outperforming the R-tree based TPRtree for both single and concurrent access scenarios.

AbstractÐWe present a new approach for indexing animated objects and efficiently answering queries about their position in time and space. In particular, we consider an animated movie as a spatiotemporal evolution. A movie is viewed as an ordered sequence of frames, where each frame is a 2D space occupied by the objects that appear in that frame. The queries of interest are range queries of the form, ªfind the objects that appear in area S between frames fi and fjº as well as nearest neighbor queries such as, ªfind the q nearest objects to a given position A between frames fi and fj.º The straightforward approach to index such objects considers the frame sequence as another dimension and uses a 3D access method (such as, an R-Tree or its variants). This, however, assigns long ªlifetimeº intervals to objects that appear through many consecutive frames. Long intervals are difficult to cluster efficiently in a 3D index. Instead, we propose to reduce the problem to a partial-persistence problem. Namely, we use a 2D access method that is made partially persistent. We show that this approach leads to faster query performance while still using storage proportional to the total number of changes in the frame evolution. What differentiates this problem from traditional temporal indexing approaches is that objects are allowed to move and/or change their extent continuously between frames. We present novel methods to approximate such object evolutions. We formulate an optimization problem for which we provide an optimal solution for the case where objects move linearly. Finally, we present an extensive experimental study of the proposed methods. While we concentrate on animated movies, our approach is general and can be applied to other spatiotemporal applications as well. Index TermsÐAccess methods, spatiotemporal databases, animated objects, multimedia. 1

With the rapid increase in the use of inexpensive, location-aware sensors in a variety of new applications, large amounts of time-sequenced location data will soon be accumulated. Efficient indexing techniques for managing these large volumes of trajectory data sets are urgently needed. The key requirements for a good trajectory indexing technique is that it must support both searches and inserts efficiently.