An efficient indexing scheme for multi-dimensional moving objects

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 O((N/B)1-1/d.(logB N)1/d + K/B) I/O\u27s using O(N/B) space, where B is the block size, and K is the number of reported points. Our approach is novel in that, while it provides a theoretical upper bound on the average query time, it avoids the use of complicated data structures, making it an effective candidate for practical applications. © Springer-Verlag Berlin Heidelberg 2003

An indexing method for answering queries on moving objects

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 O((N/B)1-1/d ·(log B N)1/d +K/B) I/O\u27s using O(N/B) space, where B is the block size, and K is the number of reported points. Our approach is novel in that, while it provides a theoretical upper bound on the average query time, it avoids the use of complicated data structures, making it an effective candidate for practical applications. The proposed index is also dynamic in the sense that it allows object insertion and deletion in an amortized update cost of log B (N) I/O\u27s. Experimental results are presented to show the superiority of the proposed index over other methods based on R-trees. © 2005 Springer Science + Business Media, Inc

An indexing method for answering queries on moving objects

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 O((N/B)1-1/d ·(log B N)1/d +K/B) I/O\u27s using O(N/B) space, where B is the block size, and K is the number of reported points. Our approach is novel in that, while it provides a theoretical upper bound on the average query time, it avoids the use of complicated data structures, making it an effective candidate for practical applications. The proposed index is also dynamic in the sense that it allows object insertion and deletion in an amortized update cost of log B (N) I/O\u27s. Experimental results are presented to show the superiority of the proposed index over other methods based on R-trees. © 2005 Springer Science + Business Media, Inc

Robust Moving Objects Detection in Lidar Data Exploiting Visual Cues

Detecting moving objects in dynamic scenes from sequences of lidar scans is an important task in object tracking, mapping, localization, and navigation. Many works focus on changes detection in previously observed scenes, while a very limited amount of literature addresses moving objects detection. The state-of-the-art method exploits Dempster-Shafer Theory to evaluate the occupancy of a lidar scan and to discriminate points belonging to the static scene from moving ones. In this paper we improve both speed and accuracy of this method by discretizing the occupancy representation, and by removing false positives through visual cues. Many false positives lying on the ground plane are also removed thanks to a novel ground plane removal algorithm. Efficiency is improved through an octree indexing strategy. Experimental evaluation against the KITTI public dataset shows the effectiveness of our approach, both qualitatively and quantitatively with respect to the state- of-the-art

Efficient MaxCount and threshold operators of moving objects

Calculating operators of continuously moving objects presents some unique challenges, especially when the operators involve aggregation or the concept of congestion, which happens when the number of moving objects in a changing or dynamic query space exceeds some threshold value. This paper presents the following six d-dimensional moving object operators: (1) MaxCount (or MinCount), which finds the Maximum (or Minimum) number of moving objects simultaneously present in the dynamic query space at any time during the query time interval. (2) CountRange, which finds a count of point objects whose trajectories intersect the dynamic query space during the query time interval. (3) ThresholdRange, which finds the set of time intervals during which the dynamic query space is congested. (4) ThresholdSum, which finds the total length of all the time intervals during which the dynamic query space is congested. (5) ThresholdCount, which finds the number of disjoint time intervals during which the dynamic query space is congested. And (6) ThresholdAverage, which finds the average length of time of all the time intervals when the dynamic query space is congested. For these operators separate algorithms are given to find only estimate or only precise values. Experimental results from more than 7,500 queries indicate that the estimation algorithms produce fast, efficient results with error under 5%

Towards a Scalable Dynamic Spatial Database System

With the rise of GPS-enabled smartphones and other similar mobile devices, massive amounts of location data are available. However, no scalable solutions for soft real-time spatial queries on large sets of moving objects have yet emerged. In this paper we explore and measure the limits of actual algorithms and implementations regarding different application scenarios. And finally we propose a novel distributed architecture to solve the scalability issues.Comment: (2012

Scalable Peer-to-Peer Indexing with Constant State

We present a distributed indexing scheme for peer to peer networks. Past work on distributed indexing traded off fast search times with non-constant degree topologies or network-unfriendly behavior such as flooding. In contrast, the scheme we present optimizes all three of these performance measures. That is, we provide logarithmic round searches while maintaining connections to a fixed number of peers and avoiding network flooding. In comparison to the well known scheme Chord, we provide competitive constant factors. Finally, we observe that arbitrary linear speedups are possible and discuss both a general brute force approach and specific economical optimizations