# GSMNet: A Hierarchical Graph Model for Moving Objects in Networks

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## Abstract

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## 1. Introduction

- A hierarchical GSMNet model for moving objects in networks is proposed that represents moving objects’ trajectories, underlying networks and semantic information, including social relationships and traffic, in an integrated manner. It provides an effective and unified means to handle these unstructured data.
- Based on the GSMNet model, a large set of data types and corresponding operators is provided, and we give the formal definitions of data types together with the operation signatures and semantics. Seventeen benchmark queries from BerlinMOD are rewritten in formal SQL-like notation.
- Extensive experiments with simulated trajectories generated by BerlinMOD are conducted to evaluate the efficiency and performance. The results demonstrate that our proposed GSMNet model has strong potential to reduce time-consuming table join operations and has the capability to represent the semantic information.

## 2. Related Work

## 3. GSMNet Model

#### 3.1. Preliminaries

**(1) Basic Types**

**(2) Temporal Types**

**(3) Geometry Types**

#### 3.2. Modeling Networks

#### 3.3. Moving Object Representation

**(4) Segment**

**(5) Segment Graph**

**(6) Traffic State**

**(7) Route**

**(8) Route Graph**

#### 3.4. Moving Object Representation

**(9) Moving Object**

**(10) Object Graph**

**(11) Object’s Position**

#### 3.5. Trajectory Representation

**(12) Moving Vector**

**(13) Trajectory Unit**

**(14) Trajectory**

**(15) Move Graph**

## 4. Operators

**(1) Select**

**(2) nodevalues**

**(3) getnodes**

**(4) getrajectory**

**(5) getsegments**

**(6) getmos**

**(7) getlen**

**(8) atinstants**

**(9) atperiods**

**(10) exinstants**

**(11) distance**

## 5. Benchmark Queries

## 6. Experiments

#### 6.1. Experimental Settings

#### 6.2. Experimental Results

#### 6.3. Discussion

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 5.**Heat Map of Experimental Data with Different Scalefactors: scalefactor 0.05 (

**a**), scalefactor 0.2 (

**b**) and scalefactor 1.0 (

**c**).

**Figure 6.**Comparison of GSMNet and Secondo with Different Scalefactors: scalefactor 0.05 (

**a**), scalefactor 0.2 (

**b**) and scalefactor 1.0 (

**c**).

Operations | Signature |
---|---|

select | $\underline{{G}_{s}}\times \underline{string}\to \underline{seg}$ $\underline{{G}_{o}}\times \underline{string}\to \underline{mo}$ $\underline{{G}_{m}}\times \underline{string}\to \underline{tunit}$ |

nodevalues | $\underline{seg}\times \underline{string}\to \underline{string}$ $\underline{mo}\times \underline{string}\to \underline{string}$ $\underline{tunit}\times \underline{string}\to \underline{string}$ |

getnodes | $\underline{mo}\times \underline{string}\to \underline{mo}$ $\underline{mo}\times \underline{string}\to \underline{seg}$ $\underline{mo}\times \underline{string}\to \underline{tunit}$ |

getrajectory | $\underline{mo}\times \underline{instant}\to \underline{trajectory}$ |

getsegments | $\underline{{G}_{s}}\times \underline{gpos}\to \underline{seg}$ |

getmos | $\underline{{G}_{o}}\times \underline{gpos}\to \underline{mo}$ |

getlen | $\underline{tunit}\to \underline{real}$ |

atinstants | $\underline{trajectory}\times \underline{instant}\to \underline{gpos}$ |

atperiods | $\underline{trajectory}\times \underline{period}\to \underline{tunit}$ |

exinstants | $\underline{trajectory}\times \underline{point}\to \underline{instant}$ |

distance | $\underline{trajectory}\times \underline{trajectory}\to \underline{real}$ |

Object Identity | Dimension | Query Interval | Condition Type | Aggregation | |
---|---|---|---|---|---|

Q1 | known | standard | point | single | no |

Q2 | unknown | standard | point | single | yes |

Q3 | known | temporal | point | single | no |

Q4 | unknown | spatial | point | single | no |

Q5 | known | spatial | unbounded | relation | no |

Q6 | unknown | spatial-temporal | unbounded | relation | no |

Q7 | unknown | spatial | unbounded | relation | no |

Q8 | known | temporal | range | single | no |

Q9 | unknown | temporal | range | single | yes |

Q10 | known | spatial-temporal | range | relation | no |

Q11 | unknown | spatial-temporal | point | single | no |

Q12 | unknown | spatial-temporal | point | relation | no |

Q13 | unknown | spatial-temporal | range | single | no |

Q14 | unknown | spatial-temporal | range | single | no |

Q15 | unknown | spatial-temporal | range | single | no |

Q16 | unknown | spatial-temporal | range | relation | no |

Q17 | unknown | spatial | unbounded | relation | yes |

[email protected] | [email protected] | [email protected] | |
---|---|---|---|

Number of moving objects | 447 | 894 | 2000 |

Number of days | 6 | 13 | 18 |

Number of trips | 15,045 | 62,510 | 292,940 |

**Table 4.**Benchmarking the Geo-Social-Moving model for moving objects in Networks (GSMNet) model using the Berlin Moving Objects Database (BerlinMOD) in seconds. OBA, Object-Based Approach; TBA, Trip-Based Approach.

Queries | [email protected] | [email protected] | [email protected] | ||||||
---|---|---|---|---|---|---|---|---|---|

OBA | TBA | GSMNet | OBA | TBA | GSMNet | OBA | TBA | GSMNet | |

Q1 | 0.406 | 0.335 | 0.042 | 0.476 | 0.451 | 0.045 | 0.46 | 0.407 | 0.045 |

Q2 | 0.099 | 0.055 | 0.001 | 0.05 | 0.14 | 0.001 | 0.113 | 0.099 | 0.001 |

Q3 | 2.29 | 0.616 | 5.107 | 6.303 | 0.993 | 3.023 | 12.08 | 1.092 | 11.882 |

Q4 | 76.664 | 49.516 | 18.076 | 625.431 | 273.426 | 115.423 | 6232.56 | 966.393 | 6074.57 |

Q5 | 16.737 | 20.059 | 2.492 | 45.535 | 34.71 | 27.513 | 121.885 | 61.015 | 69.589 |

Q6 | 71.396 | 189.435 | 557.425 | 333.341 | 1942.071 | 1985.613 | 7032 | 53,910.502 | 9857.268 |

Q7 | 92.666 | 35.654 | 9.91 | 2325.34 | 241.182 | 44.721 | 23,324.7 | 135.724 | 5899.961 |

Q8 | 1.209 | 1.214 | 1.199 | 5.854 | 3.521 | 4.45 | 13.989 | 4.308 | 27.391 |

Q9 | 392.336 | 784.329 | 0.914 | 1102.58 | 3241.18 | 2.735 | 4791.73 | 21,730.8 | 24.056 |

Q10 | 681.937 | 221.276 | 21.933 | 3170.48 | 1189.13 | 181.455 | 23,951.8 | 16,410.2 | 5159.848 |

Q11 | 0.956 | 0.58 | 8.985 | 1.862 | 0.849 | 38.009 | 11.602 | 1.411 | 588.454 |

Q12 | 2.188 | 0.553 | 8.852 | 144.466 | 0.51 | 36.26 | 964.456 | 0.625 | 2032.107 |

Q13 | 50.376 | 45.189 | 65.378 | 426.079 | 128.682 | 224.137 | 2015.68 | 261.572 | 3806.401 |

Q14 | 2.129 | 2.02 | 64.967 | 6.444 | 3.083 | 222.48 | 138.305 | 13.075 | 1813.416 |

Q15 | 3.662 | 4.53 | 9.172 | 121.011 | 30.562 | 38.337 | 322.635 | 36.343 | 615.332 |

Q16 | 144.565 | 58.967 | 63.356 | 102.139 | 49.206 | 221.88 | 132.165 | 74.842 | 178.596 |

Q17 | 5.129 | 27.393 | 8.793 | 467.125 | 242.219 | 39.903 | 5374.08 | 1097.145 | 620.296 |

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**MDPI and ACS Style**

Zhang, H.; Lu, F. GSMNet: A Hierarchical Graph Model for Moving Objects in Networks. *ISPRS Int. J. Geo-Inf.* **2017**, *6*, 71.
https://doi.org/10.3390/ijgi6030071

**AMA Style**

Zhang H, Lu F. GSMNet: A Hierarchical Graph Model for Moving Objects in Networks. *ISPRS International Journal of Geo-Information*. 2017; 6(3):71.
https://doi.org/10.3390/ijgi6030071

**Chicago/Turabian Style**

Zhang, Hengcai, and Feng Lu. 2017. "GSMNet: A Hierarchical Graph Model for Moving Objects in Networks" *ISPRS International Journal of Geo-Information* 6, no. 3: 71.
https://doi.org/10.3390/ijgi6030071