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Randomized 3D Geographic Routing
"... Abstract—We reconsider the problem of geographic routing in wireless ad hoc networks. We are interested in local, memoryless routing algorithms, i.e. each network node bases its routing decision solely on its local view of the network, nodes do not store any message state, and the message itself can ..."
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Abstract—We reconsider the problem of geographic routing in wireless ad hoc networks. We are interested in local, memoryless routing algorithms, i.e. each network node bases its routing decision solely on its local view of the network, nodes do not store any message state, and the message itself can only carry information about O(1) nodes. In geographic routing schemes, each network node is assumed to know the coordinates of itself and all adjacent nodes, and each message carries the coordinates of its target. Whereas many of the aspects of geographic routing have already been solved for 2D networks, little is known about higherdimensional networks. It has been shown only recently that there is in fact no local memoryless routing algorithm for 3D networks that delivers messages deterministically. In this paper, we show that a cubic routing stretch constitutes a lower bound for any local memoryless routing algorithm, and propose and analyze several randomized geographic routing algorithms which work well for 3D network topologies. For unit ball graphs, we present a technique to locally capture the surface of holes in the network, which leads to 3D routing algorithms similar to the greedyfacegreedy approach for 2D networks. I.
Achieving RangeFree Localization Beyond Connectivity
"... Wireless sensor networks have been proposed for many locationdependent applications. In such applications, the requirement of low system cost prohibitsmany rangebased methods for sensor node localization; on the other hand, rangefree localization depending only on connectivity may underutilize th ..."
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Cited by 37 (5 self)
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Wireless sensor networks have been proposed for many locationdependent applications. In such applications, the requirement of low system cost prohibitsmany rangebased methods for sensor node localization; on the other hand, rangefree localization depending only on connectivity may underutilize the proximity information embedded in neighborhood sensing. In response to the above limitations, this paper presents a rangefree approach to capturing a relative distancebetween1hopneighboringnodesfromtheirneighborhood orderings that serve as unique highdimensional location signatures for nodes in the network. With little overhead, the proposed design can be conveniently applied as a transparent supporting layer for many stateoftheart connectivitybased localization solutions to achieve better positioningaccuracy. Weimplementedourdesignwiththree wellknownlocalizationalgorithmsandtesteditintwotypes ofoutdoortestbedexperiments: an850footlonglinearnetwork with 54 MICAz motes, and a regular2D networkcovering an area of 10000 square feet with 49 motes. Results show that our design helps eliminate estimation ambiguity with subhop resolution, and reduces localization errors by as much as 35%. In addition, extensive simulations reveal an interestingfeature of robustnessfor our design underunevenly distributed radio propagation path loss, and confirm itseffectivenessforlargescalenetworks. Categories andSubject Descriptors
Locating and bypassing holes in sensor networks
 Mob. Netw. Appl
"... Abstract. In real sensor network deployments, spatial distributions of sensors are usually far from being uniform. Such networks often contain regions without enough sensor nodes, which we call holes. In this paper, we show that holes are important topological features that need to be studied. In ro ..."
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Cited by 30 (2 self)
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Abstract. In real sensor network deployments, spatial distributions of sensors are usually far from being uniform. Such networks often contain regions without enough sensor nodes, which we call holes. In this paper, we show that holes are important topological features that need to be studied. In routing, holes are communication voids that cause greedy forwarding to fail. Holes can also be defined to denote regions of interest, such as the “hot spots ” created by traffic congestion or sensor power shortage. In this paper, we define holes to be the regions enclosed by a polygonal cycle which contains all the nodes where local minima can appear. We also propose simple and distributed algorithms, the TENT rule and BOUNDHOLE, to identify and build routes around holes. We show that the boundaries of holes marked using BOUNDHOLE can be used in many applications such as geographic routing, path migration, information storage mechanisms and identification of regions of interest.
Greedy Routing with Bounded Stretch
"... Abstract—Greedy routing is a novel routing paradigm where messages are always forwarded to the neighbor that is closest to the destination. Our main result is a polynomialtime algorithm that embeds combinatorial unit disk graphs (CUDGs – a CUDG is a UDG without any geometric information) into O(log ..."
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Cited by 29 (0 self)
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Abstract—Greedy routing is a novel routing paradigm where messages are always forwarded to the neighbor that is closest to the destination. Our main result is a polynomialtime algorithm that embeds combinatorial unit disk graphs (CUDGs – a CUDG is a UDG without any geometric information) into O(log 2 n)dimensional space, permitting greedy routing with constant stretch. To the best of our knowledge, this is the first greedy embedding with stretch guarantees for this class of networks. Our main technical contribution involves extracting, in polynomial time, a constant number of isometric and balanced tree separators from a given CUDG. We do this by extending the celebrated LiptonTarjan separator theorem for planar graphs to CUDGs. Our techniques extend to other classes of graphs; for example, for general graphs, we obtain an O(log n)stretch greedy embedding into O(log 2 n)dimensional space. The greedy embeddings constructed by our algorithm can also be viewed as a constantstretch compact routing scheme in which each node is assigned an O(log 3 n)bit label. To the best of our knowledge, this result yields the best known stretchspace tradeoff for compact routing on CUDGs. Extensive simulations on random wireless networks indicate that the average routing overhead is about 10%; only few routes have a stretch above 1.5. I.
Sensor network localization by eigenvector synchronization over the Euclidean group
 In press
"... We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding and aligning uniquely realizable subsets of neighboring sensors called patches. In the noisefree case, each patch agrees with its global ..."
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Cited by 25 (15 self)
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We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding and aligning uniquely realizable subsets of neighboring sensors called patches. In the noisefree case, each patch agrees with its global positioning up to an unknown rigid motion of translation, rotation and possibly reflection. The reflections and rotations are estimated using the recently developed eigenvector synchronization algorithm, while the translations are estimated by solving an overdetermined linear system. The algorithm is scalable as the number of nodes increases, and can be implemented in a distributed fashion. Extensive numerical experiments show that it compares favorably to other existing algorithms in terms of robustness to noise, sparse connectivity and running time. While our approach is applicable to higher dimensions, in the current paper we focus on the two dimensional case.
Distributed localization using noisy distance and angle information
 PROCEEDINGS OF THE SEVENTH ACM INTERNATIONAL SYMPOSIUM ON MOBILE AD HOC NETWORKING AND COMPUTING
, 2006
"... Localization is an important and extensively studied problem in adhoc wireless sensor networks. Given the connectivity graph of the sensor nodes, along with additional local information (e.g. distances, angles, orientations etc.), the goal is to reconstruct the global geometry of the network. In th ..."
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Cited by 20 (5 self)
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Localization is an important and extensively studied problem in adhoc wireless sensor networks. Given the connectivity graph of the sensor nodes, along with additional local information (e.g. distances, angles, orientations etc.), the goal is to reconstruct the global geometry of the network. In this paper, we study the problem of localization with noisy distance and angle information. With no noise at all, the localization problem with both angle (with orientation) and distance information is trivial. However, in the presence of even a small amount of noise, we prove that the localization problem is NPhard. Localization with accurate distance information and relative angle information is also hard. These hardness results motivate our study of approximation schemes. We relax the nonconvex constraints to approximating convex constraints and propose linear programs (LP) for two formulations of the resulting localization problem, which we call the weak deployment and strong deployment problems. These two formulations give upper and lower bounds on the location uncertainty respectively: No sensor is located outside its weak deployment region, and each sensor can be anywhere in its strong deployment region without violating the approximate distance and angle constraints. Though LPbased algorithms are usually solved by centralized methods, we propose distributed, iterative methods, which are provably convergent to the centralized algorithm solutions. We give simulation results for the distributed algorithms, evaluating the convergence rate, dependence on measurement noises, and robustness to link dynamics.
Graphical Properties of Easily Localizable Sensor Networks
, 2006
"... The sensor network localization problem is one of determining the Euclidean positions of all sensors in a network given knowledge of the Euclidean positions of some, and knowledge of a number of intersensor distances. This paper identifies graphical properties which can ensure unique localizability ..."
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Cited by 18 (4 self)
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The sensor network localization problem is one of determining the Euclidean positions of all sensors in a network given knowledge of the Euclidean positions of some, and knowledge of a number of intersensor distances. This paper identifies graphical properties which can ensure unique localizability, and further sets of properties which can ensure not only unique localizability but also provide guarantees on the associated computational complexity, which can even be linear in the number of sensors on occasions. Sensor networks with minimal connectedness properties in which sensor transmit powers can be increased to increase the sensing radius lend themselves to the acquiring of the needed graphical properties. Results are presented for networks in both two and three dimensions.
Surrounding nodes in coordinatefree networks
 In Workshop in Algorithmic Foundations of Robotics
, 2006
"... Summary. Consider a network of nodes in the plane whose locations are unknown but which establish communication links based on proximity. We solve the following problems: given a node in the network, (1) determine if a given cycle surrounds the node; and (2) find some cycle that surrounds the node. ..."
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Cited by 15 (1 self)
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Summary. Consider a network of nodes in the plane whose locations are unknown but which establish communication links based on proximity. We solve the following problems: given a node in the network, (1) determine if a given cycle surrounds the node; and (2) find some cycle that surrounds the node. The only localization capabilities assumed are unique IDs with binary proximity measure, and, in some cases, cyclic orientation of neighbors. We give complete algorithms for finding and verifying surrounding cycles when cyclic orientation data is available. We also provide an efficient but noncomplete algorithm in the case where angular data is not available. 1
Sensor networks continue to puzzle: Selected open problems
 In Proc. 9th Internat. Conf. Distributed Computing and Networking (ICDCN
, 2008
"... Abstract. While several important problems in the field of sensor networks have already been tackled, there is still a wide range of challenging, open problems that merit further attention. We present five theoretical problems that we believe to be essential to understanding sensor networks. The goa ..."
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Cited by 14 (0 self)
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Abstract. While several important problems in the field of sensor networks have already been tackled, there is still a wide range of challenging, open problems that merit further attention. We present five theoretical problems that we believe to be essential to understanding sensor networks. The goal of this work is both to summarize the current state of research and, by calling attention to these fundamental problems, to spark interest in the networking community to attend to these and related problems in sensor networks.