The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees

Supowit, Kenneth J.

doi:10.1145/2402.322386

Cited by 129 publications

(62 citation statements)

References 4 publications

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“…This implies that the network constructed according to RNG will have higher accessibility than that constructed according to MST. For further reading on RNG, the readers are referred to Supowit (1983), and Jaromczyk and Toussaint (1992).…”

Section: Relevant Conceptsmentioning

confidence: 99%

“…To improve network accessibility and to avoid too many cyclical paths in the network, a relative neighbor graph (RNG) (Toussaint 1980;Jaromczyk and Toussaint 1992) was applied as the mechanism in the building of new roads. In fact, MST is a subgraph of RNG, which means that RNG has higher accessibility and smaller number of circles in the network than MST (Supowit 1983). In addition, the construction cost of road based on MST is always not the minimal (Hwang and Richards, 1992).…”

Section: Introductionmentioning

confidence: 99%

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Population-driven Urban Road Evolution Dynamic Model

Zhao

Sun

et al. 2015

Netw Spat Econ

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Abstract:In this paper, we propose a road evolution model by considering the interaction between population distribution and urban road network. In the model, new roads need to be constructed when new zones are built, and existing zones with higher population density have higher probability to connect with new roads.The relative neighborhood graph and a Fermat-Weber location problem are introduced as the connection mechanism to capture the characteristics of road evolution. The simulation experiment is conducted to demonstrate the effects of population on road evolution. Moreover, the topological attributes for the urban road network is evaluated using degree distribution, betweenness centrality, coverage, circuitness and treeness in the experiment. Simulation results show that the distribution of population in the city has a significant influence on the shape of road network, leading to a growing heterogeneous topology.

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Section: Relevant Conceptsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Population-driven Urban Road Evolution Dynamic Model

Zhao

Sun

et al. 2015

Netw Spat Econ

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“…In every triangle, the link with the greatest weight is removed. RNG is widely used and on most of utilizations the weight considered is the distance [1,12]. So, the longest edge in each triangle is removed.…”

Section: Related Workmentioning

confidence: 99%

Using Battery Level as Metric for Graph Planarization

Radak

Mitton

Simplot‐Ryl

2011

Lecture Notes in Computer Science

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Abstract. Topology control in wireless sensor networks is an important issue for scalability and energy efficiency. It is often based on graph reduction performed through the use of Gabriel Graph or Relative Neighborhood Graph. This graph reduction is usually based on geometric values. In this paper we tackle the problem of possible connectivity loss in the reduced graph by applying a battery level based reduction graph. Experiments are conducted to evaluate our proposition. Results are compared with RNG reduction which takes into account only the strength of the received signal (RSSI). Results show that our algorithm maintains network connectivity longer than solutions from the literature and balances the energy consumption over nodes.

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“…[16] 广场上,如果甲、乙两人希望成为舞伴,那么不允许存在丙同时距甲、乙更近,形式化表述为: [17] .文献 [18]证明,相对于完全图的 [19] ,这是下界,文献 [19]还给出 3 维空间的RNG计算方法,复杂度为O(N 2 ).…”

Section: Smt 定义 1(in Graphs) 给定 G=(ve)且 V={s}+{v−s}则 G 中边代价之和最低的树即unclassified

A Survey of Proximity Graphs in Wireless Networks

Lu¹,

Ming-tian²,

Niu³

et al. 2010

Journal of Software

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Network topology can be represented by the proximity graph defined as a graph with a set of vertices V and a set of edges E such that a directed edge (u,v) belong to E if and only if the point v is in the neighborhood induced by some predefined proximity measures of point u. This paper reviews some important graphs obtained so far, and the contents mainly concentrated in five aspects of those proximity graphs including their definitions or conceptions, construction algorithms, illustrations, topological relationships, and some parameters. This paper also outlines several further research directions.

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The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees

Cited by 129 publications

References 4 publications

Population-driven Urban Road Evolution Dynamic Model

Population-driven Urban Road Evolution Dynamic Model

Using Battery Level as Metric for Graph Planarization

A Survey of Proximity Graphs in Wireless Networks

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