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72
A Theory of Network Localization
, 2004
"... In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigid ..."
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Cited by 122 (12 self)
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In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.
Rigidity, Computation, and Randomization in Network Localization
 In Proceedings of IEEE INFOCOM ’04, Hong Kong
, 2004
"... In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigid ..."
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Cited by 111 (16 self)
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In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.
On the lifetime of wireless sensor networks
 TOSN
"... Network lifetime has become the key characteristic for evaluating sensor networks in an applicationspecific way. Especially the availability of nodes, the sensor coverage, and the connectivity have been included in discussions on network lifetime. Even quality of service measures can be reduced to ..."
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Cited by 72 (11 self)
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Network lifetime has become the key characteristic for evaluating sensor networks in an applicationspecific way. Especially the availability of nodes, the sensor coverage, and the connectivity have been included in discussions on network lifetime. Even quality of service measures can be reduced to lifetime considerations. A great number of algorithms and methods were proposed to increase the lifetime of a sensor network—while their evaluations were always based on a particular definition of network lifetime. Motivated by the great differences in existing definitions of sensor network lifetime that are used in relevant publications, we reviewed the state of the art in lifetime definitions, their differences, advantages, and limitations. This survey was the starting point for our work towards a generic definition of sensor network lifetime for use in analytic evaluations as well as in simulation models—focusing on a formal and concise definition of accumulated network lifetime and total network lifetime. Our definition incorporates the components of existing lifetime definitions, and introduces some additional measures. One new concept is the ability to express the service disruption tolerance of a network. Another new concept is the notion of timeintegration: in many cases, it is sufficient if a requirement is fulfilled over a certain period of time, instead of at every point in time. In addition, we combine coverage and connectivity to
On Constructing kConnected kDominating Set in Wireless Networks
 In Proceedings of the 19 th International Parallel & Distributed Processing Symposium (IPDPS
, 2005
"... An important problem in wireless ad hoc and sensor networks is to select a few nodes to form a virtual backbone that supports routing and other tasks such as area monitoring. Previous work in this area has focused on selecting a small virtual backbone for high efficiency. In this paper, we propose ..."
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Cited by 50 (1 self)
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An important problem in wireless ad hoc and sensor networks is to select a few nodes to form a virtual backbone that supports routing and other tasks such as area monitoring. Previous work in this area has focused on selecting a small virtual backbone for high efficiency. In this paper, we propose the construction of a kconnected kdominating set (kCDS) as a backbone to balance efficiency and fault tolerance. Four localized kCDS construction protocols are proposed. The first protocol randomly selects virtual backbone nodes with a given probability pk, where pk depends on the value of k and network condition, such as network size and node density. The second one maintains a fixed backbone node degree of Bk, where Bk also depends on the network condition. The third protocol is a deterministic approach. It extends Wu and Dai’s coverage condition, which is originally designed for 1CDS construction, to ensure the formation of a kCDS. The last protocol is a hybrid of probabilistic and deterministic approaches. It provides a generic framework that can convert many existing CDS algorithms into kCDS algorithms. These protocols are evaluated via a simulation study. Key words: Connected dominating set (CDS), kvertex connectivity, localized algorithms, simulation, wireless ad hoc and sensor networks. PACS: Preprint submitted to Elsevier Science 23 September 2005
Beyond Trilateration: On the Localizability of Wireless Adhoc Networks
"... Abstract — The proliferation of wireless and mobile devices has fostered the demand of context aware applications, in which location is often viewed as one of the most significant contexts. Classically, trilateration is widely employed for testing network localizability; even in many cases it wrongl ..."
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Cited by 43 (13 self)
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Abstract — The proliferation of wireless and mobile devices has fostered the demand of context aware applications, in which location is often viewed as one of the most significant contexts. Classically, trilateration is widely employed for testing network localizability; even in many cases it wrongly recognizes a localizable graph as nonlocalizable. In this study, we analyze the limitation of trilateration based approaches and propose a novel approach which inherits the simplicity and efficiency of trilateration, while at the same time improves the performance by identifying more localizable nodes. We prove the correctness and optimality of this design by showing that it is able to locally recognize all 1hop localizable nodes. To validate this approach, a prototype system with 19 wireless sensors is deployed. Intensive and largescale simulations are further conducted to evaluate the scalability and efficiency of our design. I.
Relay Placement for Higher Order Connectivity in Wireless Sensor Networks
"... Sensors typically use wireless transmitters to communicate with each other. However, sensors may be located in a way that they cannot even form a connected network (e.g, due to failures of some sensors, or loss of battery power). In this paper we consider the problem of adding the smallest number o ..."
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Cited by 39 (2 self)
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Sensors typically use wireless transmitters to communicate with each other. However, sensors may be located in a way that they cannot even form a connected network (e.g, due to failures of some sensors, or loss of battery power). In this paper we consider the problem of adding the smallest number of additional (relay) nodes so that the induced communication graph is 2connected 1. The problem is NPhard. In this paper we develop O(1)approximation algorithms that find close to optimal solutions in time O((kn) 2) for achieving kedge connectivity of n nodes. The worst case approximation guarantee is 10, but the algorithm produces solutions that are far better than this bound suggests. We also consider extensions to higher dimensions, and the scheme that we develop for points in the plane, yields a bound of 2dMST where dMST is the maximum degree of a minimumdegree Minimum Spanning Tree in d dimensions using Euclidean metrics. In addition, our methods extend with the same approximation guarantees to a generalization when the locations of relays are required to avoid certain polygonal regions (obstacles). We also prove that if the sensors are uniformly and identically distributed in a unit square, the expected number of relay nodes required goes to zero as the number of sensors goes to infinity.
MobilitySensitive Topology Control in Mobile Ad Hoc Networks
 Proc. IEEE Int’l Parallel and Distributed Processing Symp
, 2004
"... Abstract—In most existing localized topology control protocols for mobile ad hoc networks (MANETs), each node selects a few logical neighbors based on location information and uses a small transmission range to cover those logical neighbors. Transmission range reduction conserves energy and bandwidt ..."
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Cited by 34 (8 self)
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Abstract—In most existing localized topology control protocols for mobile ad hoc networks (MANETs), each node selects a few logical neighbors based on location information and uses a small transmission range to cover those logical neighbors. Transmission range reduction conserves energy and bandwidth consumption, while still maintaining network connectivity. However, the majority of these approaches assume a static network without mobility. In a mobile environment network connectivity can be compromised by two types of “bad ” location information: inconsistent information, which makes a node select too few logical neighbors, and outdated information, which makes a node use too small a transmission range. In this paper, we first show some issues in existing topology control. Then, we propose a mobilitysensitive topology control method that extends many existing mobilityinsensitive protocols. Two mechanisms are introduced: consistent local views that avoid inconsistent information and delay and mobility management that tolerate outdated information. The effectiveness of the proposed approach is confirmed through an extensive simulation study. Index Terms—Connectivity, mobile ad hoc networks (MANETs), mobility management, simulation, topology control, view consistency. æ 1
Reliable Density Estimates for Coverage and Connectivity in Thin Strips of Finite Length
, 2007
"... Deriving the critical density (which is equivalent to deriving the critical radius or power) to achieve coverage and/or connectivity for random deployments is a fundamental problem in the area of wireless networks. The probabilistic conditions normally derived, however, have limited appeal among pra ..."
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Cited by 32 (4 self)
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Deriving the critical density (which is equivalent to deriving the critical radius or power) to achieve coverage and/or connectivity for random deployments is a fundamental problem in the area of wireless networks. The probabilistic conditions normally derived, however, have limited appeal among practitioners because they are often asymptotic, i.e., they only make high probability guarantees in the limit of large system sizes. Such conditions are not very useful in practice since deployment regions are always finite. Another major limitation of most existing work on coverage and connectivity is their focus on thick deployment regions (such as a square or a disk). There is no existing work (including traditional percolation theory) that derives critical densities for thin strips (or annuli). In this paper, we address both of these shortcomings by introducing new techniques for deriving reliable density estimates for finite regions (including thin strips). We apply our techniques to solve the open problem of deriving reliable density estimates for achieving barrier coverage and connectivity in thin strips, where sensors are deployed as a barrier to detect moving objects and phenomena. We use simulations to show that our estimates are accurate even for small deployment regions. Our techniques bridge the gap between theory and practice in the area of coverage and connectivity, since the results can now be readily used in reallife deployments.
Variable radii connected sensor cover in sensor networks
 in Proc. of the IEEE International Conference on Sensor and Ad Hoc Communications and Networks (SECON
, 2004
"... Abstract—One of the useful approaches to exploit redundancy in a sensor network is to keep active only a small subset of sensors that are sufficient to cover the region required to be monitored. The set of active sensors should also form a connected communication graph, so that they can autonomously ..."
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Cited by 25 (2 self)
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Abstract—One of the useful approaches to exploit redundancy in a sensor network is to keep active only a small subset of sensors that are sufficient to cover the region required to be monitored. The set of active sensors should also form a connected communication graph, so that they can autonomously respond to application queries and/or tasks. Such a set of active sensor is known as a connected sensor cover, and the problem of selecting a minimum connected sensor cover has been well studied when the transmission radius and sensing radius of each sensor is fixed. In this article, we address the problem of selecting a minimum energycost connected sensor cover, when each sensor node can vary its sensing and transmission radius; larger sensing or transmission radius entails higher energy cost. For the above problem, we design various centralized and distributed algorithms, and compare their performance through extensive experiments. One of the designed centralized algorithms (called CGA) is shown to perform within an O(log n) factor of the optimal solution, where n is the size of the network. We have also designed a localized algorithm based on Voronoi diagrams which is empirically shown to perform very close to CGA, and due to its communicationefficiency results in significantly prolonging the sensor network lifetime. I.