A New Statistical Approach to Geographic Variation Analysis

Gabriel, K. Ruben; Sokal, Robert R.

doi:10.2307/2412323

Cited by 1,016 publications

(544 citation statements)

References 17 publications

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“…Strict Gabriel graphs can be considered to be the spherical analogue of the standard Gabriel graphs [3,12]. They will be used to prove Theorem 2 on strict double-normals.…”

Section: Gabriel Graphs and Delaunay Tilings On The Spherementioning

confidence: 99%

Double-normal pairs in the plane and on the sphere

Pach

Swanepoel

2014

Beitr Algebra Geom

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A double-normal pair of a finite set S of points from Euclidean space is a pair of points {p, q} from S such that S lies in the closed strip bounded by the hyperplanes through p and q that are perpendicular to pq. A double-normal pair pq is strict if S \ {p, q} lies in the open strip. We answer a question of Martini and Soltan (2006) by showing that a set of n ≥ 3 points in the plane has at most 3 n/2 double-normal pairs. This bound is sharp for each n ≥ 3.In a companion paper, we have asymptotically determined this maximum for points in R 3 . Here we show that if the set lies on some 2-sphere, it has at most 17n/4 − 6 double-normal pairs. This bound is attained for infinitely many values of n.We also establish tight bounds for the maximum number of strict double-normal pairs in a set of n points in the plane and on the sphere.

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“…Strict Gabriel graphs can be considered to be the spherical analogue of the standard Gabriel graphs [3,12]. They will be used to prove Theorem 2 on strict double-normals.…”

Section: Gabriel Graphs and Delaunay Tilings On The Spherementioning

confidence: 99%

Double-normal pairs in the plane and on the sphere

Pach

Swanepoel

2014

Beitr Algebra Geom

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“…Consider Figure 4, x tries to reach D in perimeter mode. The packet will eventually loop around face 3 with no intersecting point closer than p. Had the cross edge ut been removed, the packet would travel the exterior face u, s, x, v, t, and w to reach D. Given that perimeter mode must operate on planar graphs to avoid routing loops, GPSR provided two distributed algorithms that produce Relative Neighborhood Graph (RNG) [9] and [10] which are known to be planar. Both RNG and GG algorithms yield a connected planar graph so long as the connectivity between two nodes obeys the unit graph assumption: for any two vertices, they must be connected by an edge if the distance between them is less than or equal to some threshold distance d and must not be connected by an edge if the distance between them is greater than d. However, the unit graph assumption is not true in VANETs due to channel fading (obstacles and mobility).…”

Section: Geographic (Position-based) Routingmentioning

confidence: 99%

Survey of Various Protocols in Geographical Based Routing in Vehicular Adhoc Networks

Soni¹,

Tiwari²

2013

IJCATR

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: Vehicular Ad hoc Network (VANET), a subclass of mobile ad hoc networks (MANETs), is a promising approach for the intelligent transportation system (ITS). The design of routing protocols in VANETs is important and necessary issue for support the smart ITS. The key difference of VANET and MANET is the special mobility pattern and rapidly changeable topology. It is not effectively applied the existing routing protocols of MANETs into VANETs VANET (Vehicular Ad-hoc Network) is a new technology which has taken enormous attention in the recent years. Due to rapid topology changing and frequent disconnection makes it difficult to design an efficient routing protocol for routing data among vehicles, called V2V or vehicle to vehicle communication and vehicle to road side infrastructure, called V2I. The existing routing protocols for VANET are not efficient to meet every traffic scenarios. Thus design of an efficient routing protocol has taken significant attention. So, it is very necessary to identify the pros and cons of routing protocols which can be used for further improvement or development of any new routing protocol. The easiest way to classify the geographic routing protocolsis by type of routing (Unicast, Broadcast or Geocast). Other way to classify them is by the use that the protocol gives to the position information (Packet forwarding, Route Selection, Cluster formation, Formation of cells, Classify Forwarding Group, or RouteRequest Forwarding). For this survey we will use the type of routing classification and in each protocol we'll talk about how the protocol uses the geographic information.

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“…When a node has no neighbor closer to the destination, greedy is replaced by one of existing planar graph traversal algorithms [12], [22], [14], [13], [18]. Since the representation of the network is not always a planar graph, this class of strategies uses a distributed planarization algorithm, like those proposed in [21], [7], [11]. The performances of these strategies depend on two factors: the graph traversal and the distributed planarization algorithms.…”

Section: State Of the Art And Comparisonmentioning

confidence: 99%

Geographic Routing with Early Obstacles Detection and Avoidance in Dense Wireless Sensor Networks

Moraru

Leone

Nikoletseas

et al. 2008

Lecture Notes in Computer Science

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Abstract. Existing geographic routing algorithms for sensor networks are mainly concerned with finding a path toward a destination, without explicitly addressing the impact of obstacles on the routing performance. When the size of the communication voids is increased, they might not scale well with respect to the quality of paths, measured in terms of hop count and path length. This paper introduces a routing algorithm with early obstacle detection and avoidance. The routing decisions are based on path optimality evaluation, made at the node level, gradually over time. We implement our algorithm and evaluate different aspects: message delivery performance, topology control overhead and algorithm convergence time. The simulation findings demonstrate that our algorithm manages to improve significantly and quite fast the path quality while keeping the computational complexity and message overhead low. The algorithm is fully distributed, and uses only limited local network knowledge.

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A New Statistical Approach to Geographic Variation Analysis

Cited by 1,016 publications

References 17 publications

Double-normal pairs in the plane and on the sphere

Double-normal pairs in the plane and on the sphere

Survey of Various Protocols in Geographical Based Routing in Vehicular Adhoc Networks

Geographic Routing with Early Obstacles Detection and Avoidance in Dense Wireless Sensor Networks

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