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37
Navigation on a Poisson point process
 RR, n o 5790, INRIA, Rocquencourt
, 2006
"... On a locally finite point set, a navigation defines a path through the point set from a point to another. The set of paths leading to a given point defines a tree, the navigation tree. In this article, we analyze the properties of the navigation tree when the point set is a Poisson point process on ..."
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On a locally finite point set, a navigation defines a path through the point set from a point to another. The set of paths leading to a given point defines a tree, the navigation tree. In this article, we analyze the properties of the navigation tree when the point set is a Poisson point process on R d. We examine the local weak convergence of the navigation tree, the asymptotic average of a functional along a path, the shape of the navigation tree and its topological ends. We illustrate our work in the small world graphs where new results are established. AMS Classification: Primary 60D05, 05C05; secondary 90C27, 60G55.
Relaxed Gabriel graphs
 In Proc. Canadian Conf. on Computational Geometry
, 2009
"... We study a new family of geometric graphs that interpolate between the Delaunay triangulation and the Gabriel graph. These graphs share many properties with βskeletons for β ∈ [0, 1] (such as sublinear spanning ratio) with the added benefit of planarity (and consequently linear size and local routa ..."
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We study a new family of geometric graphs that interpolate between the Delaunay triangulation and the Gabriel graph. These graphs share many properties with βskeletons for β ∈ [0, 1] (such as sublinear spanning ratio) with the added benefit of planarity (and consequently linear size and local routability). 1
AGEM: Adaptive GreedyCompass Energyaware Multipath Routing Protocol for WMSNs
 In Proceedings of the 7th IEEE Consumer Communications and Networking Conference (CCNC ‘10), Las Vegas, NV, USA, 9–12
, 2010
"... Abstract—This paper presents an Adaptive GreedyCompass Energyaware Multipath (AGEM), a novel routing protocol for wireless multimedia sensors networks (WMSNs). AGEM uses sensors nodes position to make packet forwarding decisions. These decisions are made online, at each forwarding node in such a w ..."
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Abstract—This paper presents an Adaptive GreedyCompass Energyaware Multipath (AGEM), a novel routing protocol for wireless multimedia sensors networks (WMSNs). AGEM uses sensors nodes position to make packet forwarding decisions. These decisions are made online, at each forwarding node in such a way that there is no need for global network topology knowledge and maintenance. AGEM routing protocol performs loadbalancing to minimize energy consumption among nodes using twofold policy: (1) smart greedy forwarding based on adaptive compass and (2) walking back forwarding to avoid holes. Performances evaluations of AGEM compared to GPSR (Greedy Perimeter Stateless Routing) show that it can maximize the network lifetime, guarantee quality of service for video stream transmission, and scale better on densely deployed wireless sensors network.
Streaming Multimedia over WMSNs: An Online Multipath Routing Protocol
 International Journal of Sensor Networks (IJSNet
, 2012
"... Abstract: Routing has become an important challenge to Wireless Multimedia Sensor Networks (WMSNs) from the standpoint of supporting multimedia applications due to the constraints on energy and computational capabilities of sensor nodes, and acquiring of the global network knowledge for disseminatin ..."
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Abstract: Routing has become an important challenge to Wireless Multimedia Sensor Networks (WMSNs) from the standpoint of supporting multimedia applications due to the constraints on energy and computational capabilities of sensor nodes, and acquiring of the global network knowledge for disseminating packets to nodes. In this paper, we propose an online multipath routing protocol for use in WMSNs. The proposed protocol uses sensor nodes ’ positions to make packetforwarding decisions at each hop. These decisions are made in realtime, in such a way that there is no need for having the knowledge about the entire network topology. This new routing protocol achieves loadbalancing of traffic and minimizes energy consumption among nodes by using: (1) smart greedy forwarding scheme based on adaptive compass for selecting the most appropriate next hop for forwarding the traffic and (2) walking back forwarding scheme to bypass network holes. Performance comparison of the proposed protocols with TwoPhase Geographical Greedy Forwarding (TPGF) and Greedy Perimeter Stateless Routing (GPSR) shows that they: (a) maximize the overall network lifespan by not draining energy from some specific nodes, (b) provide quality of service delivery for video streams by influencing the best node along
Efficient Delaunaybased Localized Routing for Wireless Sensor Networks
"... Consider a wireless sensor network consisting of n wireless sensors randomly distributed in a twodimensional plane. In this paper, we show that with high probability we can locally find a path for any pair of sensors such that the length of the path is no more than a constant factor of the minimum. ..."
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Consider a wireless sensor network consisting of n wireless sensors randomly distributed in a twodimensional plane. In this paper, we show that with high probability we can locally find a path for any pair of sensors such that the length of the path is no more than a constant factor of the minimum. By assuming each sensor knows its position, our new routing method decides where to forward the message purely based on the position of current node, its neighbors, and the positions of the source and the target. Our method is based on a novel structure called localized Delaunay triangulation [1] and a geometric routing method [2] that guarantees that the distance traveled by the packets is no more than a small constant factor of the minimum when the Delaunay triangulation of sensor nodes are known. Our experiments show that the delivery rates of existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies, and our localized routing protocol based on Delaunay triangulation works well in practice. We also conducted extensive simulations of another localized routing protocol, face routing [13]. The path found by this protocol is also reasonably good compared with previous one although it cannot guarantee a constant approximation on the length of the path traveled theoretically. Copyright c ○ 2000 John Wiley & Sons, Ltd. key words: Wireless sensor networks, Delaunay triangulation, localized routing, power efficiency.
Computing the detour and spanning ratio of paths, trees and cycles in 2d and 3d. Discrete & Computational Geometry
"... The detour and spanning ratio of a graph embedded in measure how well approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms, we ob ..."
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The detour and spanning ratio of a graph embedded in measure how well approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms, we obtaintime algorithms for computing the detour or spanning ratio of planar trees and cycles. Finally, we develop subquadratic algorithms for computing the detour and spanning ratio for paths, cycles, and trees embedded! in, and show that computing the detour "! in is at least as hard as Hopcroft’s problem.
Bluetooth Scatternet Formation for SingleHop Ad Hoc Networks Based on Virtual Positions
 IN ‘IEEE SYMPOSIUM ON COMPUTERS AND COMMUNICATIONS
, 2004
"... This paper addresses the problem of scatternet formation for singlehop Bluetooth based personal area and ad hoc networks, with minimal communication overhead. In a singlehop ad hoc network, all wireless devices are in the radio vicinity of each other, e.g., electronic devices in a laboratory, or ..."
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This paper addresses the problem of scatternet formation for singlehop Bluetooth based personal area and ad hoc networks, with minimal communication overhead. In a singlehop ad hoc network, all wireless devices are in the radio vicinity of each other, e.g., electronic devices in a laboratory, or laptops in a conference room. Recent scatternet formation schemes by Li, Stojmenovic and Wang [1] are position based and were applied for multihop networks. These schemes are localized and can construct degree limited and connected piconets, without parking any node. They also limit to 7 the number of slave roles in one piconet. The creation and maintenance require small overhead in addition to maintaining location information for onehop neighbors. In this article we apply this method to singlehop networks, by showing that position information is then not needed. Each node can simply select a virtual position, and communicate it to all neighbors in the neighbor discovery phase. Nodes then act according to the scheme by Li, Stojmenovic and Wang using such virtual positions instead of real ones. In addition, in this paper we use Delaunay triangulation instead of partial Delaunay triangulation proposed in [1], since each node has all the information needed. Likewise, we can also apply Minimum Spanning Tree (MST) as the planar topology in our new schemes. Finally, we design experiments to study both the properties of formatted scatternet (such as number
Quality Guaranteed Localized Routing for Wireless Ad Hoc Networks
, 2003
"... We consider a wireless ad hoc network consisting of n points randomly distributed in a twodimensional plane. We show that, with high probability, we can find a path for any pair of nodes locally such that the length of the path is no more than a constant factor of the minimum. By assuming each node ..."
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Cited by 1 (0 self)
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We consider a wireless ad hoc network consisting of n points randomly distributed in a twodimensional plane. We show that, with high probability, we can find a path for any pair of nodes locally such that the length of the path is no more than a constant factor of the minimum. By assuming each node knows its position, the method decides where to forward the message purely based on the positions of current node, its neighbors, and the positions of the source and the target. Our method is based on a novel structure called localized Delaunay triangulation [1] and an efficient localized routing method [2] that guarantees that the distance traveled by the packets is no more than a small constant factor of the minimum when the Delaunay triangulation of wireless nodes are known. Our experiments show that the delivery rates of existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies, and the localized routing protocol based on Delaunay triangulation works well in practice. We also conducted extensive simulations of another localized routing protocol, FACE method [3]. The path found by this protocol is also reasonably good compared with previous one although it cannot guarantee a constant approximation on the length of the path traveled theoretically. I.
Routing with Guaranteed Delivery . . .
, 2006
"... We propose four simple algorithms for routing on planar graphs using virtual coordinates. These algorithms are superior to existing algorithms in that they are oblivious, work also for nontriangular graphs, and their virtual coordinates are easy to construct. ..."
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We propose four simple algorithms for routing on planar graphs using virtual coordinates. These algorithms are superior to existing algorithms in that they are oblivious, work also for nontriangular graphs, and their virtual coordinates are easy to construct.