# A Line Graph-Based Continuous Range Query Method for Moving Objects in Networks

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## Abstract

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## 1. Introduction

- We develop a novel graph-based expansion tree (GET) based on the line graph model of networks. It supports offline pre-computation and could effectively reduce the online maintenance time of the traditional expansion tree in continuous queries.
- Based on GET, we propose a line graph-based continuous range (LGCR) query algorithm for moving objects in networks, including the algorithms for initialization, insertion, location update, filter and refinement.
- We conducted experiments to evaluate our proposed LGCR using real-world networks and simulated moving objects and compare with existing classical algorithms to verify its effectiveness.

## 2. Related Work

## 3. Proposed Data Structures

## 4. LGCR Query Algorithm

#### 4.1. Algorithms

Algorithm 1: Initialization algorithm. |

Algorithm 2: Insertion of moving objects and query objects. |

Algorithm 3: Filter and refinement step. |

Algorithm 4: Location update of a moving object or query object. |

#### 4.2. Analysis of the Algorithm’s Complexity

## 5. Experiments

#### 5.1. Experimental Settings

#### 5.2. Experimental Results

#### 5.3. Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**An example of bridgeable edges. (

**a**) A query object in network; (

**b**) The schematic of bridgeable edges

**Figure 7.**GT-MobiSIM. (

**a**) The simultion with 5000 moving objects and 500 query objects; (

**b**) The simultion with 10,000 moving objects and 1000 query objects.

**Figure 10.**Comparison of Stojanovic continuous range (StojanovicCR) and line graph-based continuous range (LGCR). (

**a**) The result of the experiment with 5000 moving objects and 500 query objects; (

**b**) The result of the experiment with 10,000 moving objects and 1000 query objects.

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**MDPI and ACS Style**

Zhang, H.; Lu, F.; Chen, J.
A Line Graph-Based Continuous Range Query Method for Moving Objects in Networks. *ISPRS Int. J. Geo-Inf.* **2016**, *5*, 246.
https://doi.org/10.3390/ijgi5120246

**AMA Style**

Zhang H, Lu F, Chen J.
A Line Graph-Based Continuous Range Query Method for Moving Objects in Networks. *ISPRS International Journal of Geo-Information*. 2016; 5(12):246.
https://doi.org/10.3390/ijgi5120246

**Chicago/Turabian Style**

Zhang, Hengcai, Feng Lu, and Jie Chen.
2016. "A Line Graph-Based Continuous Range Query Method for Moving Objects in Networks" *ISPRS International Journal of Geo-Information* 5, no. 12: 246.
https://doi.org/10.3390/ijgi5120246