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87
Geometric Spanner for Routing in Mobile Networks
, 2001
"... Abstract—We propose a new routing graph, the restricted Delaunay graph (RDG), for mobile ad hoc networks. Combined with a node clustering algorithm, the RDG can be used as an underlying graph for geographic routing protocols. This graph has the following attractive properties: 1) it is planar; 2) be ..."
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Cited by 153 (19 self)
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Abstract—We propose a new routing graph, the restricted Delaunay graph (RDG), for mobile ad hoc networks. Combined with a node clustering algorithm, the RDG can be used as an underlying graph for geographic routing protocols. This graph has the following attractive properties: 1) it is planar; 2) between any two graph nodes there exists a path whose length, whether measured in terms of topological or Euclidean distance, is only a constant times the minimum length possible; and 3) the graph can be maintained efficiently in a distributed manner when the nodes move around. Furthermore, each node only needs constant time to make routing decisions. We show by simulation that the RDG outperforms previously proposed routing graphs in the context of the Greedy perimeter stateless routing (GPSR) protocol. Finally, we investigate theoretical bounds on the quality of paths discovered using GPSR. Index Terms—Geographical routing, spanners, wireless ad hoc networks. I.
Coverage in Wireless Adhoc Sensor Networks
, 2002
"... Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking [1]. One of the fundamental problems in sensor networks is the calculation of the coverage. In [1], it is assumed that the sensor has the uniform sensing ability. In this pape ..."
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Cited by 113 (9 self)
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Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking [1]. One of the fundamental problems in sensor networks is the calculation of the coverage. In [1], it is assumed that the sensor has the uniform sensing ability. In this paper, we give efficient distributed algorithms to optimally solve the bestcoverage problem raised in [1]. Here, we consider the sensing model: the sensing ability diminishes as the distance increases. As energy conservation is a major concern in wireless (or sensor) networks, we also consider how to find an optimum bestcoverage path with the least energy consumption. We also consider how to find an optimum bestcoveragepath that travels a small distance. In addition, we justify the correctness of the method proposed in [1] that uses the Delaunay triangulation to solve the best coverage problem. Moreover, we show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.
AdHoc Networks Beyond Unit Disk Graphs
, 2003
"... In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer ..."
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Cited by 101 (10 self)
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In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that  in comparison to the cost known on Unit Disk Graphs  the complexity results in this model contain the additional factor 1/d². We prove that in Quasi Unit Disk Graphs flooding is an asymptotically messageoptimal routing technique, provide a geometric routing algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d 1/ # 2.
Asymptotically Optimal Geometric Mobile AdHoc Routing
, 2002
"... In this paper we present AFR, a new geometric mobile adhoc routing algorithm. The algorithm is completely distributed; nodes need to communicate only with direct neighbors in their transmission range. We show that if a best route has cost c, AFR finds a route and terminates with cost O(c ) in the ..."
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Cited by 99 (12 self)
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In this paper we present AFR, a new geometric mobile adhoc routing algorithm. The algorithm is completely distributed; nodes need to communicate only with direct neighbors in their transmission range. We show that if a best route has cost c, AFR finds a route and terminates with cost O(c ) in the worst case. AFR is the first algorithm with cost bounded by a function of the optimal route. We also give a tight lower bound by showing that any geometric routing algorithm has worstcase ). Thus AFR is asymptotically optimal. We give a nongeometric algorithm that also matches the lower bound, but needs some memory at each node. This establishes an intriguing tradeo# between geometry and memory.
Does Topology Control Reduce Interference
 In Proceedings of the 5 th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC
, 2004
"... Topology control in adhoc networks tries to lower node energy consumption by reducing transmission power and by confining interference, collisions and consequently retransmissions. Commonly low interference is claimed to be a consequence to sparseness of the resulting topology. In this paper we dis ..."
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Cited by 89 (8 self)
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Topology control in adhoc networks tries to lower node energy consumption by reducing transmission power and by confining interference, collisions and consequently retransmissions. Commonly low interference is claimed to be a consequence to sparseness of the resulting topology. In this paper we disprove this implication. In contrast to most of the related work—claiming to solve the interference issue by graph sparseness without providing clear argumentation or proofs—, we provide a concise and intuitive definition of interference. Based on this definition we show that most currently proposed topology control algorithms do not effectively constrain interference. Furthermore we propose connectivitypreserving and spanner constructions that are interferenceminimal.
Topology Control meets SINR: The Scheduling Complexity of Arbitrary Topologies
 In Proc. of the 7 th ACM Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC
, 2006
"... To date, topology control in wireless ad hoc and sensor networks—the study of how to compute from the given communication network a subgraph with certain beneficial properties—has been considered as a static problem only; the time required to actually schedule the links of a computed topology withou ..."
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Cited by 73 (8 self)
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To date, topology control in wireless ad hoc and sensor networks—the study of how to compute from the given communication network a subgraph with certain beneficial properties—has been considered as a static problem only; the time required to actually schedule the links of a computed topology without message collision was generally ignored. In this paper we analyze topology control in the context of the physical SignaltoInterferenceplusNoiseRatio (SINR) model, focusing on the question of how and how fast the links of a resulting topology can actually be realized over time. For this purpose, we define and study a generalized version of the SINR model and obtain theoretical upper bounds on the scheduling complexity of arbitrary topologies in wireless networks. Specifically, we prove that even in worstcase networks, if the signals are transmitted with correctly assigned transmission power levels, the number of time slots required to successfully schedule all links of an arbitrary topology is proportional to the squared logarithm of the number of network nodes times a previously defined static interference measure. Interestingly, although originally considered without explicit accounting for signal collision in the SINR model, this static interference measure plays an important role in the analysis of link scheduling with physical link interference. Our result thus bridges the gap between static graphbased interference models and the physical SINR model. Based on these results, we also show that when it comes to scheduling, requiring the communication links to be symmetric may imply significantly higher costs as opposed to topologies allowing unidirectional links.
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
 In DIALMPOMC
, 2003
"... We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to know its 2hop neighbors to find the edges in this new structure. Our method applies the Yao structure on the local Delauna ..."
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Cited by 69 (8 self)
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We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to know its 2hop neighbors to find the edges in this new structure. Our method applies the Yao structure on the local Delaunay graph [21] in an ordering that are computed locally. This new structure has the following attractive properties: (1) it is a planar graph; (2) its node degree is bounded from above by a positive constant 19 + ⌈ 2π α ⌉; (3) it is a tspanner (given any two nodes u and v, there is a path connecting them in the structure such that its length is no more than t ≤ max { π α,πsin 2 2 +1}·Cdel times of the shortest path in UDG); (4) it can be constructed locally and is easy to maintain when the nodes move around; (5) moreover, we show that the total communication cost is O(n), where n is the number of wireless nodes, and the computation cost of each node is at most O(d log d), where d is its 2hop neighbors in the original unit disk graph. Here Cdel is the spanning ratio of the Delaunay triangulation, which is at most 4 √ 3 9 π. And the adjustable parameter α satisfies 0 <α<π/3. In addition, experiments are conducted to show this topology is efficient in practice, compared with other wellknown topologies used in wireless ad hoc networks. Previously, only centralized method [5] of constructing bounded degree planar spanner is known, with degree bound 27 and spanning ratio t ≃ 10.02. The distributed implementation of their centralized method takes O(n 2) communications in the worst case. No localized methods were known previously for constructing bounded degree planar spanner.
On delivery guarantees of face and combined greedyface routing in ad hoc and sensor networks
 in Ad Hoc and Sensor Networks”. In Proc. of ACM MobiCom
, 2006
"... It was recently reported that all known face and combined greedyface routing variants cannot guarantee message delivery in arbitrary undirected planar graphs. The purpose of this article is to clarify that this is not the truth in general. We show that specifically in relative neighborhood and Gabr ..."
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Cited by 68 (13 self)
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It was recently reported that all known face and combined greedyface routing variants cannot guarantee message delivery in arbitrary undirected planar graphs. The purpose of this article is to clarify that this is not the truth in general. We show that specifically in relative neighborhood and Gabriel graphs recovery from a greedy routing failure is always possible without changing between any adjacent faces. Guaranteed delivery then follows from guaranteed recovery while traversing the very first face. In arbitrary graphs, however, a proper face selection mechanism is of importance since recovery from a greedy routing failure may require visiting a sequence of faces before greedy routing can be restarted again. A prominent approach is to visit a sequence of faces which are intersected by the line connecting the source and destination node. Whenever encountering an edge which is intersecting with this line, the critical part is to decide if face traversal has to change to the next adjacent one or not. Failures may occur from incorporating face routing procedures that force to change the traversed face at each intersection. Recently observed routing failures which were produced by the GPSR protocol in arbitrary planar graphs result from incorporating such a face routing variant. They cannot be constructed by the well known GFG algorithm which does not force changing the face anytime. Beside methods which visit the faces intersected by the source destination line, we discuss face routing variants which simply restart face routing whenever the next face has to be explored. We give the first complete and formal proofs that several proposed face routing, and combined greedyface routing schemes do guarantee delivery in specific graph classes or even any arbitrary planar graphs. We also discuss the reasons why other methods may fail to deliver a message or even end up in a loop.
XTC: A Practical Topology Control Algorithm for AdHoc Networks
 In 4th International Workshop on Algorithms for Wireless, Mobile, Ad Hoc and Sensor Networks (WMAN
, 2003
"... The XTC adhoc network topology control algorithm introduced in this paper shows three main advantages over previously proposed algorithms. First, it is extremely simple and strictly local. Second, it does not assume the network graph to be a Unit Disk Graph; XTC proves correct also on general weigh ..."
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Cited by 64 (9 self)
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The XTC adhoc network topology control algorithm introduced in this paper shows three main advantages over previously proposed algorithms. First, it is extremely simple and strictly local. Second, it does not assume the network graph to be a Unit Disk Graph; XTC proves correct also on general weighted network graphs. Third, the algorithm does not require availability of node position information. Instead, XTC operates with a general notion of order over the neighbors' link qualities. In the special case of the network graph being a Unit Disk Graph, the resulting topology proves to have bounded degree, to be a planar graph, andon averagecase graphsto be a good spanner.
Geometric Spanners for Wireless Ad Hoc Networks
 IEEE Transactions on Parallel and Distributed Systems
, 2003
"... We propose a new geometric spanner for static wireless ad hoc networks, which can be constructed efficiently in a localized manner. It integrates the connected dominating set and the local Delaunay graph to form a backbone of the wireless network. ..."
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Cited by 64 (16 self)
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We propose a new geometric spanner for static wireless ad hoc networks, which can be constructed efficiently in a localized manner. It integrates the connected dominating set and the local Delaunay graph to form a backbone of the wireless network.