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R.: The Complexity of Connectivity in Wireless Networks
 In: Proc. of the 25 th Annual Joint Conf. of the IEEE Computer and Communications Societies (INFOCOM
, 2006
"... Abstract — We define and study the scheduling complexity in wireless networks, which expresses the theoretically achievable efficiency of MAC layer protocols. Given a set of communication requests in arbitrary networks, the scheduling complexity describes the amount of time required to successfully ..."
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Cited by 69 (12 self)
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Abstract — We define and study the scheduling complexity in wireless networks, which expresses the theoretically achievable efficiency of MAC layer protocols. Given a set of communication requests in arbitrary networks, the scheduling complexity describes the amount of time required to successfully schedule all requests. The most basic and important network structure in wireless networks being connectivity, we study the scheduling complexity of connectivity, i.e., the minimal amount of time required until a connected structure can be scheduled. In this paper, we prove that the scheduling complexity of connectivity grows only polylogarithmically in the number of nodes. Specifically, we present a novel scheduling algorithm that successfully schedules a strongly connected set of links in time O(log 4 n) even in arbitrary worstcase networks. On the other hand, we prove that standard MAC layer or scheduling protocols can perform much worse. Particularly, any protocol that either employs uniform or linear (a node’s transmit power is proportional to the minimum power required to reach its intended receiver) power assignment has a Ω(n) scheduling complexity in the worst case, even for simple communication requests. In contrast, our polylogarithmic scheduling algorithm allows many concurrent transmission by using an explicitly formulated nonlinear power assignment scheme. Our results show that even in largescale worstcase networks, there is no theoretical scalability problem when it comes to scheduling transmission requests, thus giving an interesting complement to the more pessimistic bounds for the capacity in wireless networks. All results are based on the physical model of communication, which takes into account that the signaltonoise plus interference ratio (SINR) at a receiver must be above a certain threshold if the transmission is to be received correctly. I.
Localized Topology Control for Heterogeneous Wireless Adhoc Networks
"... We study topology control in heterogeneous wireless ad hoc networks, where mobile hosts may have different maximum transmission powers and two nodes are connected iff they are within the maximum transmission range of each other. We present several strategies that all wireless nodes selfmaintain sp ..."
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Cited by 46 (8 self)
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We study topology control in heterogeneous wireless ad hoc networks, where mobile hosts may have different maximum transmission powers and two nodes are connected iff they are within the maximum transmission range of each other. We present several strategies that all wireless nodes selfmaintain sparse and power efficient topologies in heterogeneous network environment with low communication cost. The first structure is sparse and can be used for broadcasting. While the second structure keeps the minimum power consumption path, and the third structure is a length and power spanner with a bounded degree. Both the second and third structures are power efficient and can be used for unicast. Here a structure is power efficient if the total power consumption of the least cost path connecting any two nodes in it is no more than a small constant factor of that in the original heterogeneous communication graph. All our methods use at most O(n) total messages, where each message has O(log n) bits.
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 24 (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
The kneighbors approach to interference bounded and symmetric topology control in ad hoc networks
 IEEE Trans. on Mobile Computing
, 2006
"... Topology control, wherein nodes adjust their transmission ranges to conserve energy and reduce interference, is an important feature in wireless ad hoc networks. Contrary to most of the literature on topology control which focuses on reducing energy consumption, in this paper we tackle the topolog ..."
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Cited by 15 (1 self)
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Topology control, wherein nodes adjust their transmission ranges to conserve energy and reduce interference, is an important feature in wireless ad hoc networks. Contrary to most of the literature on topology control which focuses on reducing energy consumption, in this paper we tackle the topology control problem with the goal of limiting interference as much as possible, while keeping the communication graph connected with high probability. Our approach is based on the principle of maintaining the number of physical neighbors of every node equal to or slightly below a specific value k. As we will discuss in this paper, having a nontrivially bounded physical node degree allows a network topology with bounded interference to be generated. The proposed approach enforces symmetry on the resulting communication graph, thereby easing the operation of higher layer protocols. To evaluate the performance of our approach, we estimate the value of k that guarantees connectivity of the communication graph with high probability both theoretically and through simulation. We then define kNeigh, a fully distributed, asynchronous, and localized protocol that uses distance estimation. kNeigh guarantees logarithmically bounded physical degree at every node, is the most efficient known protocol (requiring 2n messages in total, where
Bootstrapping a Hopoptimal Network in the Weak Sensor Model
 In Proc. of the 13th Annual European Symposium on Algorithms, volume 3669 of Lecture Notes in Computer Science
, 2005
"... Sensor nodes are very weak computers that get distributed at random on a surface. Once deployed, they must wake up and form a radio network. Sensor network bootstrapping research thus has three parts: one must model the restrictions on sensor nodes; one must prove that the connectivity graph of ..."
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Cited by 13 (10 self)
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Sensor nodes are very weak computers that get distributed at random on a surface. Once deployed, they must wake up and form a radio network. Sensor network bootstrapping research thus has three parts: one must model the restrictions on sensor nodes; one must prove that the connectivity graph of the sensors has a subgraph that would make a good network; and one must give a distributed protocol for finding such a network subgraph that can be implemented on sensor nodes.
Distributed algorithms for constructing approximate minimum spanning trees with applications to wireless sensor networks
 THE IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS (TPDS). HTTP://WWW.CS.PURDUE.EDU/HOMES/MMKHAN/PAPERS/TPDS.PDF
"... The Minimum Spanning Tree (MST) problem is an important and commonly occurring primitive in the design and operation of data and communication networks. While there are distributed algorithms for the MST problem, these algorithms require relatively large number of messages and time, and are fairly i ..."
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Cited by 12 (5 self)
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The Minimum Spanning Tree (MST) problem is an important and commonly occurring primitive in the design and operation of data and communication networks. While there are distributed algorithms for the MST problem, these algorithms require relatively large number of messages and time, and are fairly involved, require synchronization and a lot of book keeping; this makes these algorithms impractical for resourceconstrained networks such as ad hoc wireless sensor networks. In such networks, a sensor has very limited power, and any algorithm needs to be simple, local, and energy efficient for being practical. Motivated by these considerations, we design and analyze a class of simple and local distributed algorithms called Nearest Neighbor Tree (NNT) algorithms for energyefficient construction of MSTs in a wireless ad hoc setting. We assume that the nodes are uniformly distributed in a unit square and show provable bounds on the performance with respect to both the quality of the spanning tree produced and the energy needed to construct them. In particular, we show that NNT produces a close approximation to the MST, and they can be maintained dynamically with polylogarithmic number of rearrangements under node insertions/deletions. We also perform extensive simulations of our algorithms. We tested our algorithms on both uniformly random distributions of nodes, and on a realistic distributions of nodes in an urban setting. Simulations validate
Constant density spanners for wireless ad hoc networks
 In Proc. of SPAA ’05
, 2005
"... An important problem for wireless ad hoc networks has been to design overlay networks that allow time and energyefficient routing. Many localcontrol strategies for maintaining such overlay networks have already been suggested, but most of them are based on an oversimplified wireless communication ..."
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Cited by 9 (5 self)
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An important problem for wireless ad hoc networks has been to design overlay networks that allow time and energyefficient routing. Many localcontrol strategies for maintaining such overlay networks have already been suggested, but most of them are based on an oversimplified wireless communication model. In this paper, we suggest a model that is much more general than previous models. It allows the path loss of transmissions to significantly deviate from the idealistic unit disk model and does not even require the path loss to form a metric. Also, our model is apparently the first proposed for algorithm design that does not only model transmission and interference issues but also aims at providing a realistic model for physical carrier sensing. Physical carrier sensing is needed so that our protocols do not require any prior information (not even an estimate on the number of nodes) about the
Virtual Backbone Construction in MANETs using Adjustable Transmission Ranges
 Mobile Computing, IEEE Transactions on
, 2006
"... Recently, the use of a virtual backbone in various applications in mobile ad hoc networks (MANETs) has become popular. These applications include topology management, point and area coverage, and routing protocol design. In a MANET, one challenging issue is to construct a virtual backbone in a distr ..."
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Cited by 6 (2 self)
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Recently, the use of a virtual backbone in various applications in mobile ad hoc networks (MANETs) has become popular. These applications include topology management, point and area coverage, and routing protocol design. In a MANET, one challenging issue is to construct a virtual backbone in a distributed and localized way while balancing several conflicting objectives: small approximation ratio, fast convergence, and low computation cost. Many existing distributed and localized algorithms select a virtual backbone without resorting to global or geographical information. However, these algorithms incur a high computation cost in a dense network. In this paper, we propose a distributed solution based on reducing the density of the network using two mechanisms: clustering and adjustable transmission range. By using adjustable transmission range, we also achieve another objective, energyefficient design, as a byproduct. As an application, we show an efficient broadcast scheme where nodes (and only
F.: Separability and Topology Control of Quasi Unit Disk Graphs
 In: Proc. 26th IEEE International Conference on Computer Communications INFOCOM 2007
, 2007
"... Abstract — A deep understanding of the structural properties of wireless networks is critical for evaluating the performance of network protocols and improving their designs. Many protocols for wireless networks — routing, topology control, information storage/retrieval and numerous other applicatio ..."
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Cited by 5 (0 self)
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Abstract — A deep understanding of the structural properties of wireless networks is critical for evaluating the performance of network protocols and improving their designs. Many protocols for wireless networks — routing, topology control, information storage/retrieval and numerous other applications — have been based on the idealized unitdisk graph (UDG) network model. The significant deviation of the UDG model from many real wireless networks is substantially limiting the applicability of such protocols. A more general network model, the quasi unitdisk graph (quasiUDG) model, captures much better the characteristics of wireless networks. However, the understanding of the properties of general quasiUDGs has been very limited, which is impeding the designs of key network protocols and algorithms. In this paper, we present results on two important properties of quasiUDGs: separability and the existence of power efficient spanners. Network separability is a fundamental property leading to efficient network algorithms and fast parallel computation. We prove that every quasiUDG has a corresponding grid graph with small balanced separators that captures its connectivity properties. We also study the problem of constructing an energyefficient backbone for a quasiUDG. We present a distributed localized algorithm that, given a quasiUDG, constructs a nearly planar backbone with a constant stretch factor and a bounded degree. We demonstrate the excellent performance of these auxiliary graphs through simulations and show their applications in efficient routing. I.
Initializing sensor networks of nonuniform density in the weak sensor model
 In Proc. of 10th International Workshop on Algorithms and Data Structures
, 2007
"... Abstract. Assumptions about node density in the Sensor Networks literature are frequently too strong or too weak. Neither absolutely arbitrary nor uniform deployment seem feasible in most of the intended applications of sensor nodes. We present a Weak Sensor Modelcompatible distributed protocol for ..."
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Cited by 5 (5 self)
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Abstract. Assumptions about node density in the Sensor Networks literature are frequently too strong or too weak. Neither absolutely arbitrary nor uniform deployment seem feasible in most of the intended applications of sensor nodes. We present a Weak Sensor Modelcompatible distributed protocol for hopoptimal network initialization, under the assumption that the maximum density of nodes is some value ∆ known by all of the nodes. In order to prove lower bounds, we observe that all nodes must communicate with some other node in order to join the network, and we call the problem of achieving such a communication the Group Therapy Problem. We show lower bounds for the Group Therapy Problem in Radio Networks of maximum density ∆, regardless of the use of randomization, and a stronger lower bound for the important class of randomized fair protocols. We also show that even when nodes are distributed uniformly, the same lower bound holds, even in expectation and even for the simpler problem of Clear Transmission. 1