Generation of constrained network Voronoi diagram using linear tessellation and expansion method

Ai, Tinghua; Yu, Wenhao; He, Yakun

doi:10.1016/j.compenvurbsys.2015.02.001

Cited by 24 publications

(15 citation statements)

References 25 publications

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“…In order to obtain the kernel density distribution of the entire road network, we need to split all the links in the network by a predefined segment size. The link segmentation has been a common practice for network-based analyses that need to capture the distribution of events across street network [30][31][32]34]. Therefore, we firstly divide each street segment into basic linear units of a predefined network length, and then, for a point p j on the network, its kernel density value f p j is given by the following:…”

Section: Constraint Of Fire Riskmentioning

confidence: 99%

Service Area Delimitation of Fire Stations with Fire Risk Analysis: Implementation and Case Study

Chen

et al. 2020

IJERPH

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Under the rapid development of urbanization, fire service becomes one of the biggest contributive factors to personal health and property safety. A reasonable plan of fire services should first address the issue of service area delimitation for fire emergency facilities. Specifically, there are two key factors for fire services including rescue efficiency and load balancing, which are usually handled by the space partitioning methods (e.g., Voronoi diagram). The traditional methods tend to model the space in a homogeneous plane with Euclidean distance, while in reality, the movement of rescuing is constrained by the street network. In addition, the built environment is complex by its variation of fire risk across places. Therefore, we propose a novel constrained Voronoi diagram for fire service area delimitation by adding the datasets of street network and historical fire incidents. Considering the prior knowledge that a fire engine is expected to reach the location of incident within five minutes, which is also called Golden 5 min, we propose a network partitioning algorithm which is able to increase the five-minute coverage of fire stations. Through a case study in Nanjing, China, we demonstrate the practicability of the proposed method in delimitating service areas of fire stations across time.the unbalanced built environment leads to the spatial heterogeneity of service demand. At the same time, the intricate roads have greatly affected the ability of urban services. Therefore, the traditional Voronoi diagram that models the urban space as a homogeneous environment is no longer suitable for delimiting the service areas of current urban facilities.In the literature, many extensions of the Voronoi diagram have been developed to adapt to the complexity of real-world geographic scenes. For example, Okabe et al. [18] formulate six Voronoi diagrams defined on the network, termed generalized network Voronoi diagrams, to precisely represent service areas in urban areas. The extension of the Voronoi diagram to a network space is more in line with the real characteristics of a street network service transmission and more suitable for urban activities, e.g., retail services. With considering the geographic distribution of demands and the socioeconomic context, Wang et al. [19] apply the hexagon-based adaptive crystal growth Voronoi diagrams to delimit middle school service areas. The results indicate that, compared with the raster-based method, the hexagon grid method is more accurate in measuring continuous weighted planes. Furthermore, the weighted Voronoi diagram allows for a more detailed modeling of services by introducing the varied capabilities of a facility. It is widely used in urban planning applications including trade zone design [20], transportation and logistics problems [21-23], political districting [24], substation planning [25,26], and school districting [19,27].However, there are few studies on the service division applied to urban emergency facilities, especially fire stations. As a critical emergenc...

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Section: Constraint Of Fire Riskmentioning

confidence: 99%

Service Area Delimitation of Fire Stations with Fire Risk Analysis: Implementation and Case Study

Chen

et al. 2020

IJERPH

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“…To construct weighted network Voronoi diagrams, the stream flowing method, which has been tested to be an effective method for constructing the network Voronoi diagrams, is employed here [18]. It is described step by step in the following subsections.…”

Section: Construction Of Weighted Network Voronoi Diagramsmentioning

confidence: 99%

“…The idea of stream flowing which is similar to the expansion principle in mathematical morphology is employed in expansion operations here [18]. In the process of expansion, the projected lixels of the points are viewed as the source of the generator starting from which the flows expand with a certain step along with related road segments simultaneously.…”

Section: Expansion Operatormentioning

confidence: 99%

“…Compared with the ordinary Voronoi diagram, the network Voronoi diagram is more appropriate for analyzing the spatial phenomena and activities that are constrained by networks. For example, it has been applied in analyzing traffic accidents and crime distribution and describing service regions [15][16][17][18]. Thus, it should be a natural thought to use network Voronoi diagrams to simplify the point clusters that stand for geographic entities on the Earth and are closely related to the nearby road networks.…”

Section: Introductionmentioning

confidence: 99%

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An Algorithm based on the Weighted Network Voronoi Diagram for Point Cluster Simplification

Yan

et al. 2019

IJGI

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Points on maps that stand for geographic objects such as settlements are generally connected by road networks. However, in the existing algorithms for point cluster simplification, points are usually viewed as discrete objects or their distances are considered in Euclidean spaces, and therefore the point cluster generalization results obtained by these algorithms are sometimes unreasonable. To take roads into consideration so that point clusters can be simplified in appropriate ways, the network Voronoi diagram is used and a new algorithm is proposed in this paper. First, the weighted network Voronoi diagram is constructed taking into account the weights of the points and the properties of the related road segments. Second, the network Voronoi polygons are generated and two factors (i.e., the area of the network Voronoi polygon and the total length of the dilated road segments in the polygon) are considered as the basis for point simplification. Last, a Cartesian coordinate system is built based on the two factors and the point clusters are simplified by means of the “concentric quadrants”. Our experiments show that the algorithm can effectively and correctly transmit types of information in the process of point cluster simplification, and the results are more reasonable than that generated by the ordinary Voronoi-based algorithm and the weighted Voronoi-based algorithm.

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“…found that measuring distance by connecting the straight line between locations could possibly overestimate the clustering tendency of the network. The network distance is more appropriate for spatial phenomena or activities constrained by transportation networks, especially in the field of microscopic analysis (Ai et al, 2015). Peeters and Thomas (1995) examined the performance of the p-median model in different network topologies by changing the nature of the links.…”

Section: The P-median Modelmentioning

confidence: 99%

How Does the Complexity of A Road Network Affect Optimal Facility Locations?

Zhao¹,

Rebreyend²,

Håkansson³

2019

jtle

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The road network is a necessary component in transportation. It facilities spatial movements of people and goods, and it also influences the optimal locations of facilities that usually serve as destinations of the movements. To fulfill the transportation needs and to adapt to the facility development, the road network is often organized hierarchically and asymmetrically with various road levels and spatial structures. The complexity of the road network increases along with the increase of road levels and spatial structures. However, location models locate facilities on a given road network, usually the most complex one, and the influence from the complexity of road network in finding optimal locations is not wellstudied. This paper aims to investigate how the complexity of a road network affects the optimal facility locations by applying the widely-applied p-median model. The main result indicates that an increase in road network complexity, up to a certain level, can obviously improve the solution, and the complexity beyond that level does not always lead to better solutions. Furthermore, the result is not sensitive to the choice of algorithms. In a specific case study, a detailed sensitivity analysis of algorithm and facility number further provides insight into computation complexity and location problems from intra-urban to inter-urban.

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Generation of constrained network Voronoi diagram using linear tessellation and expansion method

Cited by 24 publications

References 25 publications

Service Area Delimitation of Fire Stations with Fire Risk Analysis: Implementation and Case Study

Service Area Delimitation of Fire Stations with Fire Risk Analysis: Implementation and Case Study

An Algorithm based on the Weighted Network Voronoi Diagram for Point Cluster Simplification

How Does the Complexity of A Road Network Affect Optimal Facility Locations?

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