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58
Geometric AdHoc Routing: Of Theory and Practice
, 2003
"... All too often a seemingly insurmountable divide between theory and practice can be witnessed. In this paper we try to contribute to narrowing this gap in the field of adhoc routing. In particular we consider two aspects: We propose a new geometric routing algorithm which is outstandingly e#cient on ..."
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Cited by 235 (11 self)
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All too often a seemingly insurmountable divide between theory and practice can be witnessed. In this paper we try to contribute to narrowing this gap in the field of adhoc routing. In particular we consider two aspects: We propose a new geometric routing algorithm which is outstandingly e#cient on practical averagecase networks, however is also in theory asymptotically worstcase optimal. On the other hand we are able to drop the formerly necessary assumption that the distance between network nodes may not fall below a constant value, an assumption that cannot be maintained for practical networks. Abandoning this assumption we identify from a theoretical point of view two fundamentamentally di#erent classes of cost metrics for routing in adhoc networks.
Scalable informationdriven sensor querying and routing for ad hoc heterogeneous sensor networks
 International Journal of High Performance Computing Applications
, 2002
"... This paper describes two novel techniques, informationdriven sensor querying (IDSQ) and constrained anisotropic diffusion routing (CADR), for energyefficient data querying and routing in ad hoc sensor networks for a range of collaborative signal processing tasks. The key idea is to introduce an inf ..."
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Cited by 211 (12 self)
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This paper describes two novel techniques, informationdriven sensor querying (IDSQ) and constrained anisotropic diffusion routing (CADR), for energyefficient data querying and routing in ad hoc sensor networks for a range of collaborative signal processing tasks. The key idea is to introduce an information utility measure to select which sensors to query and to dynamically guide data routing. This allows us to maximize information gain while minimizing detection latency and bandwidth consumption for tasks such as localization and tracking. Our simulation results have demonstrated that the informationdriven querying and routing techniques are more energy efficient, have lower detection latency, and provide anytime algorithms to mitigate risks of link/node failures. 1
WorstCase Optimal and AverageCase Efficient Geometric AdHoc Routing
, 2003
"... In this paper we present GOAFR, a new geometric adhoc routing algorithm combining greedy and face routing. We evaluate this algorithm by both rigorous analysis and comprehensive simulation. GOAFR is the first adhoc algorithm to be both asymptotically optimal and averagecase e#cient. For our simul ..."
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Cited by 180 (13 self)
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In this paper we present GOAFR, a new geometric adhoc routing algorithm combining greedy and face routing. We evaluate this algorithm by both rigorous analysis and comprehensive simulation. GOAFR is the first adhoc algorithm to be both asymptotically optimal and averagecase e#cient. For our simulations we identify a network density range critical for any routing algorithm. We study a dozen of routing algorithms and show that GOAFR outperforms other prominent algorithms, such as GPSR or AFR.
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 154 (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.
ConstantTime Distributed Dominating Set Approximation
 In Proc. of the 22 nd ACM Symposium on the Principles of Distributed Computing (PODC
, 2003
"... Finding a small dominating set is one of the most fundamental problems of traditional graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary parameter k and maximum degree #, our algorithm computes a dominating set ..."
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Cited by 111 (24 self)
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Finding a small dominating set is one of the most fundamental problems of traditional graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary parameter k and maximum degree #, our algorithm computes a dominating set of expected size O k# log #DSOPT rounds where each node has to send O k messages of size O(log #). This is the first algorithm which achieves a nontrivial approximation ratio in a constant number of rounds.
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.
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 70 (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.
Initializing Newly Deployed Ad Hoc and Sensor Networks
 in Proceedings of 10 th Annual International Conference on Mobile Computing and Networking (MOBICOM
, 2004
"... A newly deployed multihop radio network is unstructured and lacks a reliable and e#cient communication scheme. In this paper, we take a step towards analyzing the problems existing during the initialization phase of ad hoc and sensor networks. Particularly, we model the network as a multihop quasi ..."
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Cited by 49 (14 self)
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A newly deployed multihop radio network is unstructured and lacks a reliable and e#cient communication scheme. In this paper, we take a step towards analyzing the problems existing during the initialization phase of ad hoc and sensor networks. Particularly, we model the network as a multihop quasi unit disk graph and allow nodes to wake up asynchronously at any time. Further, nodes do not feature a reliable collision detection mechanism, and they have only limited knowledge about the network topology. We show that even for this restricted model, a good clustering can be computed e#ciently. Our algorithm e#ciently computes an asymptotically optimal clustering. Based on this algorithm, we describe a protocol for quickly establishing synchronized sleep and listen schedule between nodes within a cluster. Additionally, we provide simulation results in a variety of settings.
Deformable spanners and applications
 In Proc. of the 20th ACM Symposium on Computational Geometry (SoCG’04
, 2004
"... For a set S of points in R d,ansspanner is a graph on S such that any pair of points is connected via some path in the spanner whose total length is at most s times the Euclidean distance between the points. In this paper we propose a new sparse (1 + ε)spanner with O(n/ε d) edges, where ε is a spe ..."
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Cited by 35 (5 self)
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For a set S of points in R d,ansspanner is a graph on S such that any pair of points is connected via some path in the spanner whose total length is at most s times the Euclidean distance between the points. In this paper we propose a new sparse (1 + ε)spanner with O(n/ε d) edges, where ε is a specified parameter. The key property of this spanner is that it can be efficiently maintained under dynamic insertion or deletion of points, as well as under continuous motion of the points in both the kinetic data structures setting and in the more realistic blackbox displacement model we introduce. Our deformable spanner succinctly encodes all proximity information in a deforming point cloud, giving us efficient kinetic algorithms for problems such as the closest pair, the near neighbors of all points, approximate nearest neighbor search (aka approximate Voronoi diagram), wellseparated pair decomposition, and approximate kcenters. 1
Clustering Motion
 In Proc. 42nd Annu. IEEE Sympos. Found. Comput. Sci
, 2003
"... Given a set of moving points in IR , we show how to cluster them in advance, using a small number of clusters, so that at any time this static clustering is competitive with the optimal kcenter clustering at that time. The advantage of this approach is that it avoids updating the clustering a ..."
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Cited by 30 (5 self)
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Given a set of moving points in IR , we show how to cluster them in advance, using a small number of clusters, so that at any time this static clustering is competitive with the optimal kcenter clustering at that time. The advantage of this approach is that it avoids updating the clustering as time passes. We also show how to maintain this static clustering eciently under insertions and deletions.