Indexing Moving Points

Distributed and Parallel Databases, 2005

We consider the problem of indexing a set of objects moving in d-dimensional spaces along linear trajectories. A simple external-memory indexing scheme is proposed to efficiently answer general range queries. The following are examples of the queries that can be answered by the proposed method: report all moving objects that will (i) pass between two given points within a specified time interval; (ii) become within a given distance from some or all of a given set of other moving objects. Our scheme is based on mapping the objects to a dual space, where queries about moving objects are transformed into polyhedral queries concerning their speeds and initial locations. We then present a simple method for answering such polyhedral queries, based on partitioning the space into disjoint regions and using a B+-tree to index the points in each region. By appropriately selecting the boundaries of each region, we guarantee an average search time that matches a known lower bound for the problem. Specifically, for a fixed d, if the coordinates of a given set of N points are statistically independent, the proposed technique answers polyhedral queries, on the average, in

Lecture Notes in Computer Science, 2002

We consider the problem of indexing a set of objects moving in d-dimensional space along linear trajectories. A simple disk-based indexing scheme is proposed to efficiently answer queries of the form: report all objects that will pass between two given points within a specified time interval. Our scheme is based on mapping the objects to a dual space, where queries about moving objects translate into polyhedral queries concerning their speeds and initial locations. We then present a simple method for answering such polyhedral queries, based on partitioning the space into disjoint regions and using a B-tree to index the points in each region. By appropriately selecting the boundaries of each region, we can guarantee an average search time that almost matches a known lower bound for the problem. Specifically, for a fixed d, if the coordinates of a given set of N points are statistically independent, the proposed technique answers polyhedral queries, on the average, in

Advances in Databases and Information Systems, 2007

We present a set of time-efficient approaches to index objects moving on the plane to efficiently answer range queries about their future positions. Our algorithms are based on previously described solutions as well as on the employment of efficient data structures. Finally, an experimental evaluation is included that shows the performance, scalability and efficiency of our methods.

GeoInformatica, 2003

A desirable feature in spatio-temporal databases is the ability to answer future queries, based on the current data characteristics (reference position and velocity vector). Given a moving query and a set of moving objects, a future query asks for the set of objects that satisfy the query in a given time interval. The difficulty in such a case is that both the query and the data objects change positions continuously, and therefore we can not rely on a given fixed reference position to determine the answer. Existing techniques are either ...

Eighth International Conference on Database Systems for Advanced Applications, 2003. (DASFAA 2003). Proceedings., 2003

Moving object environments contain large numbers of queries and continuously moving objects. Traditional spatial index structures do not work well in this environment because of the need to frequently update the index which results in very poor performance. In this paper, we present a novel indexing structure, namely the Q+Rtree, based on the observation that i) most moving objects are in quasi-static state most of time, and ii) the moving patterns of objects are strongly related to the topography of the space. The Q+Rtree is a hybrid tree structure which consists of both an R-tree and a QuadTree. The Rtree component indexes quasi-static objects-those that are currently moving slowly and are often crowded together in buildings or houses. The Quadtree component indexes fast moving objects which are dispersed over wider regions. We also present the experimental evaluation of our approach.

Proceedings of the 6th international conference on Mobile data management, 2005

Although significant effort has been put into the development of efficient spatio-temporal indexing techniques for moving objects, little attention has been given to the development of techniques that efficiently support queries about the past, present, and future positions of objects. The provisioning of such techniques is challenging, both because of the nature of the data, which reflects continuous movement, and because of the types of queries to be supported. This paper proposes the BB x-index structure, which indexes the positions of moving objects, given as linear functions of time, at any time. The index stores linearized moving-object locations in a forest of B +-trees. The index supports queries that select objects based on temporal and spatial constraints, such as queries that retrieve all objects whose positions fall within a spatial range during a set of time intervals. Empirical experiments are reported that offer insight into the query and update performance of the proposed technique.

ACM Transactions on Algorithms, 2012

We propose designing data structures called succinct geometric indexes of negligible space (more precisely, o ( n ) bits) that support geometric queries in optimal time, by taking advantage of the n points in the dataset permuted and stored elsewhere as a sequence. Our first and main result is a succinct geometric index that can answer point location queries, a fundamental problem in computational geometry, on planar triangulations in O (lg n ) time. We also design three variants of this index. The first supports point location using lg n + 2√lg n + O (lg 1/4 n ) point-line comparisons. The second supports point location in o (lg n ) time when the coordinates are integers bounded by U . The last variant can answer point location queries in O ( H + 1) expected time, where H is the entropy of the query distribution. These results match the query efficiency of previous point location structures that occupy O ( n ) words or O(n lg n ) bits, while saving drastic amounts of space. We gene...

Sigmod Record, 2000

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Lecture Notes in Computer Science, 2004

The ability to represent and query continuously moving objects is important in many applications of spatio-temporal database systems. In this paper we develop data structures for answering various queries on moving objects, including range and proximity queries, and study tradeoffs between various performance measures-query time, data structure size, and accuracy of results.

2009

Mobile query processing is, currently, a very active research field. Range and nearest neighbor queries are commonly used in spatiotemporal databases and location based services (LBS). In this paper, we focus on finding nearest neighbors of a query point within a certain distance range. We propose a new indexing structure CN-tree, Compact N-tree, based on a recent indexing technique called N-tree. CN-tree joins efficiency of N-tree's data partitioning scheme to pertinent objects' approximation with minimal bounding rectangles of R-trees which are reported to be the best performing for range search. We show how we use the approximation in constructing CN-tree and, then, how this index can support range queries efficiently by minimizing computation of distances and avoiding overlapping of minimal bounding rectangles. The experimental results through the comparison with the well know R*-tree, show that the proposed CN-tree widely outperforms R*-tree as an in-memory index and it presents competitive performances when used as an in-disk index.