The promotion / demotion algorithm of moving objects with large velocity differences in time-parameterized spatio-temporal index

Highlights

• The hybrid tree index structures uses a new velocity-based dynamic leveling policy that can store speed outlier objects on a non-leaf node in the tree.

Abstract

Overlapping costs increase due to a difference in speed of moving objects, ranging from low-speed submarines to high-speed airplanes in the time-parameterized spatio-temporal index. This paper proposes a new method for promoting fast moving objects to upper non-leaf nodes to minimize overlap when the speed difference between objects in the index is considerably large. Experimental evaluation on datasets of moving objects with large speed differences demonstrates that the performance of insertion and deletion is improved. Our results show that the performance of the prediction query with speed parameters is improved by 75.8% as compared to previous approaches.

Introduction

The military information system (MIS) is a network-centric enterprise service that integrates several combat systems, such as various sensor systems, command and control systems, and striking systems on land, sea, and in the air, to share tactical situations of an entire battlefield and execute cooperative operations with different combat systems. To effectively operate the command, control, communication, and intelligence for military operations, it is important to collect, store, and manage tactical moving objects in real-time [1], [2]. Tactical objects consist of moving objects, such as missiles, fighters, helicopters, surface ships, destroyer ships, patrol ships, fishing ships, submarines, and other objects of security intelligence.

Tactical moving objects are identified through various sensor systems, such as radar, sonar, optical sensor, infrared sensor, and automatic navigation equipment mounted on a unit combat system that observes the operations of a subordinate unit. These combat systems report identified objects to the MIS system periodically through a tactical data network. The MIS system then synthesizes and processes the stream data gathered from individual unit combat systems to decide on subsequent tactical operations. Unlike individual radar and sonar systems, the time required to update information on moving objects through the tactical data network of the MIS system ranges from a few seconds to several tens of seconds. The reason behind this is that the MIS system has to deal with hundreds of unit combat systems.

A database of tactical moving objects is required to use a spatio-temporal index to insert, delete, and update objects in real-time. The total number of moving objects stored in the database and the number of objects that need to be updated at the same time is in the order of tens of thousands to hundreds of thousands. The speed of these moving objects varies from 10 km/h to more than 1000 km/h [3].

The most important challenge is to identify moving objects to be included in a given spatial region within a future time interval [4], [5], [6]. To date, the best spatio-temporal index for predictive query performance over future time intervals is termed TPR*-trees [7], [8]. To solve the problem of real-time update and insertion, which is a limitation of both the TPR*-tree and the R-Tree [9], several methods of directly pointing to the leaf nodes of the TPR*-tree, using an object ID with a hashmap or Quadtree, were proposed [10], [11], [12]. The Q＋Rtree [12] was proposed as a method of combining the Quadtree and the R-Tree to support the rapid update of moving objects. To solve frequent changes in index structure based on the TPR-tree, a method of using a secondary index was proposed [10], [11], [13]. In this study, we add this secondary index to point the moving object on the tree with a hashmap without searching the location of the moving object.

This paper presents a new approach for inserting fast moving objects into non-leaf nodes to effectively support real-time insertion and update when the speed difference between moving objects is large. The existing approach [12], [14], [15], [16] that creates k indexes for each speed range cannot support real-time updating at high speed differences between moving objects, owing to the cost of joint processing. The idea of placing a high-speed object at the upper node of an index tree rather than using a speed-based index partitioning method [14], [15] is the novelty of this study. This study proposes a hierarchically velocity-based leveling of moving objects in index nodes to minimize the cost of the ChooseSubtree function for prediction query processing of moving objects with large speed differences.

The novel approach presented in this paper reduces overlapping due to the Minimum Bounding Rectangle (MBR) expansion, allowing the storage of data entries of fast-moving objects in non-leaf nodes. We compare the method of storing data of fast-moving objects in a leaf node with the method of storing the same data in non-leaf nodes. We show that the overlapping of the TPR*-tree can be reduced by storing fast moving objects in non-leaf nodes. The reason for storing fast moving objects in non-leaf nodes is that the MBR can be rapidly expanded over time by fast moving objects, potentially increasing overlapping.

Because the TPR*-tree usually consists of indexing nodes that are leveled hierarchically, it is necessary to develop a new method to choose an optimal non-leaf node to store a moving object by jointly considering both the speed of the object and the MBR of the child nodes included in the corresponding non-leaf node. To determine whether to store fast moving objects (we call this speed outlier) on non-leaf nodes or leaf nodes, different criteria are needed, depending on the distribution of moving objects in a given MBR. The increase in overlapping cost before and after promoting a speed outlier is used to decide whether or not to allocate the speed outlier to non-leaf nodes. When storing a speed outlier object in a non-leaf node, we not only use its speed as a criterion, but the increase in overlap due to the inclusion of the speed outlier object is calculated as a cost function.

We expect two benefits of storing fast moving objects in non-leaf nodes. First, the search performance of the index does not deteriorate because the overlapping ratio of the MBR of the non-leaf nodes decreases even though the MBR, due to the fast-moving object, rapidly expands. Second, the number of non-leaf nodes visited during index search is considerably reduced because the fast object has already been searched for before visiting the leaf node. These two benefits ensure that the prediction query performance does not deteriorate, even though the index contains fast moving objects.

The main contribution of this study is that it proposes a new velocity-based dynamic leveling policy for reducing overlapping of non-leaf nodes. This reduces the overlap of the MBR by reducing MBR expansion caused by fast moving objects, thereby contributing toward the improvement of search performance. The experimental results indicate that the search performance of the proposed dynamic promotion policy is better than that of the original TPR*-tree.

Section 2 defines the problem of the effects of fast-moving objects on the index. Section 3 describes a velocity-based dynamic leveling policy for storing fast moving objects in non-leaf nodes. The algorithms of insertion, deletion, updating, and search are described in Section 4. Section 5 describes the performance analysis, and Section 6 describes how the results differ from those of previous studies. Section 7 discusses the inferences.