TL;DR: This work presents a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks, and shows that this approach can take advantage of redundant network capacity for improved success probability and robustness.
Abstract: We present a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks. Network nodes independently and randomly select linear mappings from inputs onto output links over some field. We show that this achieves capacity with probability exponentially approaching 1 with the code length. We also demonstrate that random linear coding performs compression when necessary in a network, generalizing error exponents for linear Slepian-Wolf coding in a natural way. Benefits of this approach are decentralized operation and robustness to network changes or link failures. We show that this approach can take advantage of redundant network capacity for improved success probability and robustness. We illustrate some potential advantages of random linear network coding over routing in two examples of practical scenarios: distributed network operation and networks with dynamically varying connections. Our derivation of these results also yields a new bound on required field size for centralized network coding on general multicast networks
TL;DR: A new distributed energy-efficient clustering scheme for heterogeneous wireless sensor networks, which is called DEEC, is proposed and evaluated, which achieves longer lifetime and more effective messages than current important clustering protocols in heterogeneous environments.
TL;DR: In this article, a system for monitoring and configuring gaming devices interconnected over a high speed network is described, which can support a file server, one or more floor controllers, and other terminals all interconnected over the network.
Abstract: A system for monitoring and configuring gaming devices interconnected over a high-speed network is disclosed. The system can support a file server, one or more floor controllers, one or more pit terminals, and other terminals all interconnected over the network. Each gaming device includes an electronic module which allows the gaming device to communicate with a floor controller over a current loop network. The electronic module includes a player tracking module and a data communication node. The player tracking module includes a card reader for detecting a player tracking card inserted therein which identifies the player. The data communication node communicates with both the floor controller and the gaming device. The data communication node communicates with the gaming device over a serial interface through which the data communication node transmits reconfiguration commands. The gaming device reconfigures its payout schedule responsive to the reconfiguration commands to provide a variety of promotional bonuses such as multiple jackpot bonuses, mystery jackpot bonuses, progressive jackpot bonuses, or player specific bonuses.
TL;DR: The security of LEAP+ under various attack models is analyzed and it is shown that it is very effective in defending against many sophisticated attacks, such as HELLO flood attacks, node cloning attacks, and wormhole attacks.
Abstract: We describe LEAPp (Localized Encryption and Authentication Protocol), a key management protocol for sensor networks that is designed to support in-network processing, while at the same time restricting the security impact of a node compromise to the immediate network neighborhood of the compromised node. The design of the protocol is motivated by the observation that different types of messages exchanged between sensor nodes have different security requirements, and that a single keying mechanism is not suitable for meeting these different security requirements. LEAPp supports the establishment of four types of keys for each sensor node: an individual key shared with the base station, a pairwise key shared with another sensor node, a cluster key shared with multiple neighboring nodes, and a global key shared by all the nodes in the network. LEAPp also supports (weak) local source authentication without precluding in-network processing. Our performance analysis shows that LEAPp is very efficient in terms of computational, communication, and storage costs. We analyze the security of LEAPp under various attack models and show that LEAPp is very effective in defending against many sophisticated attacks, such as HELLO flood attacks, node cloning attacks, and wormhole attacks. A prototype implementation of LEAPp on a sensor network testbed is also described.
TL;DR: In this paper, a system and methods for organizing and querying data within a linear grid management system is presented, where data having multiple dimensions are associated with physical locations, where a first dimension is associated with a node and a second dimension associated with the data storage identifier of a memory storage device.
Abstract: A system and methods for organizing and querying data within a linear grid management system. Data having multiple dimensions is associated with physical locations, where a first dimension is associated with a node and a second dimension is associated with a data storage identifier of a memory storage device. The data may have a third dimension which provides a field for ordering data within the memory storage device. Metadata may be used to map a logical table to data stored in the memory storage device. The data query may be divided into multiple subqueries, wherein each subquery is related directly to one node associated with a data storage identifier related to a memory storage device. A preSQL and postSQL process may be generated to access an external database. A dispatcher may manage data subrequests and a node may generate a unique and efficient parsing process from the received data subrequest.
TL;DR: In this article, a control system is coupled to a node and distribution network for delivering to the node at least one characteristic of the distribution network, and the node for controlling the supply of energy to the device as a function of the characteristics.
Abstract: A system and method manage delivery of energy from a distribution network to one or more sites. Each site has at least one device coupled to the distribution network. The at least one device controllably consumes energy. The system includes a node and a control system. The node is coupled to the at least one device for sensing and controlling energy delivered to the device. A control system is coupled to the node and distribution network for delivering to the node at least one characteristic of the distribution network. The node for controls the supply of energy to the device as a function of the at least one characteristic.
TL;DR: An Aloha-type access control mechanism for large mobile, multihop, wireless networks is defined and analyzed and it can be implemented in a decentralized way provided some local geographic information is available to the mobiles.
Abstract: An Aloha-type access control mechanism for large mobile, multihop, wireless networks is defined and analyzed. This access scheme is designed for the multihop context, where it is important to find a compromise between the spatial density of communications and the range of each transmission. More precisely, the analysis aims at optimizing the product of the number of simultaneously successful transmissions per unit of space (spatial reuse) by the average range of each transmission. The optimization is obtained via an averaging over all Poisson configurations for the location of interfering mobiles, where an exact evaluation of signal over noise ratio is possible. The main mathematical tools stem from stochastic geometry and are spatial versions of the so-called additive and max shot noise processes. The resulting medium access control (MAC) protocol exhibits some interesting properties. First, it can be implemented in a decentralized way provided some local geographic information is available to the mobiles. In addition, its transport capacity is proportional to the square root of the density of mobiles which is the upper bound of Gupta and Kumar. Finally, this protocol is self-adapting to the node density and it does not require prior knowledge of this density.
TL;DR: The conclusion is that building scalable mobile UWSNs is a challenge that must be answered by interdisciplinary efforts of acoustic communications, signal processing, and mobile acoustic network protocol design.
Abstract: The large-scale mobile underwater wireless sensor network (UWSN) is a novel networking paradigm to explore aqueous environments. However, the characteristics of mobile UWSNs, such as low communication bandwidth, large propagation delay, floating node mobility, and high error probability, are significantly different from ground-based wireless sensor networks. The novel networking paradigm poses interdisciplinary challenges that will require new technological solutions. In particular, in this article we adopt a top-down approach to explore the research challenges in mobile UWSN design. Along the layered protocol stack, we proceed roughly from the top application layer to the bottom physical layer. At each layer, a set of new design intricacies is studied. The conclusion is that building scalable mobile UWSNs is a challenge that must be answered by interdisciplinary efforts of acoustic communications, signal processing, and mobile acoustic network protocol design.
TL;DR: A scalable, distributed weighted-multidimensional scaling (dwMDS) algorithm that adaptively emphasizes the most accurate range measurements and naturally accounts for communication constraints within the sensor network is introduced.
Abstract: Accurate, distributed localization algorithms are needed for a wide variety of wireless sensor network applications. This article introduces a scalable, distributed weighted-multidimensional scaling (dwMDS) algorithm that adaptively emphasizes the most accurate range measurements and naturally accounts for communication constraints within the sensor network. Each node adaptively chooses a neighborhood of sensors, updates its position estimate by minimizing a local cost function and then passes this update to neighboring sensors. Derived bounds on communication requirements provide insight on the energy efficiency of the proposed distributed method versus a centralized approach. For received signal-strength (RSS) based range measurements, we demonstrate via simulation that location estimates are nearly unbiased with variance close to the Cramer-Rao lower bound. Further, RSS and time-of-arrival (TOA) channel measurements are used to demonstrate performance as good as the centralized maximum-likelihood estimator (MLE) in a real-world sensor network.
TL;DR: A medium access control (MAC) protocol suitable for an underwater acoustic network is proposed and analyzed, which uses time slotting and is thus called slotted FAMA, thus providing savings in energy.
Abstract: Long propagation delays and low bit rates of underwater acoustic networks make these systems fundamentally different from the packet radio networks. As a consequence, many of the network protocols designed for radio channels are either not applicable, or have extremely low efficiency over underwater acoustic channels. These facts necessitate a dedicated design of protocols for an underwater acoustic network. A medium access control (MAC) protocol suitable for an underwater acoustic network is proposed and analyzed. The protocol is based on a channel access discipline called floor acquisition multiple access (FAMA) which combines both carrier sensing (CS) and a dialogue between the source and receiver prior to data transmission. During the initial dialogue, control packets are exchanged between the source node and the intended destination node to avoid multiple transmissions at the same time. Special attention is paid to the networks that are not fully connected, in which nodes can be hidden from each other. The new protocol uses time slotting and is thus called slotted FAMA. Time slotting eliminates the need for excessively long control packets, thus providing savings in energy. Protocol performance in throughput and delay is assessed through simulation of a mobile ad hoc underwater network, showing the existence of optimal power level to be used for a given user density.
TL;DR: In this paper, the authors present an automatic configuration management of a network by determining an inventory of resources at a virtualization layer of a node of the network, assigning prioritization to members of a set of network configuration elements and allocating virtual resources among the set of configuration elements, establishing a network configuration.
Abstract: Automatic configuration management of a network is provided by determining an inventory of resources at a virtualization layer of a node of the network, assigning prioritization to members of a set of network configuration elements, allocating virtual resources among the set of network configuration elements, establishing a network configuration. The configuration is managed by determining real time performance metrics for the configuration, producing a reallocation of the virtual resources based on the performance metrics that are estimated to change the established configuration, change the performance metrics, and initiating the reallocation of the virtual resources. This Abstract is provided for the sole purpose of complying with the Abstract requirement that allows a reader to quickly ascertain the subject matter of the disclosure contained herein. This Abstract is submitted with the understanding that it will not be used to interpret or to limit the scope or the meaning of the claims.
TL;DR: This work presents fast and cheap attacks that reveal the location of a hidden server, the first actual intersection attacks on any deployed public network: thus confirming general expectations from prior theory and simulation.
Abstract: Hidden services were deployed on the Tor anonymous communication network in 2004. Announced properties include server resistance to distributed DoS. Both the EFF and Reporters Without Borders have issued guides that describe using hidden services via Tor to protect the safety of dissidents as well as to resist censorship. We present fast and cheap attacks that reveal the location of a hidden server. Using a single hostile Tor node we have located deployed hidden servers in a matter of minutes. Although we examine hidden services over Tor, our results apply to any client using a variety of anonymity networks. In fact, these are the first actual intersection attacks on any deployed public network: thus confirming general expectations from prior theory and simulation. We recommend changes to route selection design and implementation for Tor. These changes require no operational increase in network overhead and are simple to make; but they prevent the attacks we have demonstrated. They have been implemented.
TL;DR: A strategy based on two principles: layouts are based on user-defined semantic substrates, which are non-overlapping regions in which node placement is based on node attributes, and users interactively adjust sliders to control link visibility to limit clutter and thus ensure comprehensibility of source and destination.
Abstract: Networks have remained a challenge for information visualization designers because of the complex issues of node and link layout coupled with the rich set of tasks that users present. This paper offers a strategy based on two principles: (1) layouts are based on user-defined semantic substrates, which are non-overlapping regions in which node placement is based on node attributes, (2) users interactively adjust sliders to control link visibility to limit clutter and thus ensure comprehensibility of source and destination. Scalability is further facilitated by user control of which nodes are visible. We illustrate our semantic substrates approach as implemented in NVSS 1.0 with legal precedent data for up to 1122 court cases in three regions with 7645 legal citations
TL;DR: In this paper, the stationary spatial distribution of a node moving according to the random waypoint model in a given convex area is analyzed, which is in the form of a one-dimensional integral giving the density up to a normalization constant.
Abstract: The random waypoint model (RWP) is one of the most widely used mobility models in performance analysis of ad hoc networks. We analyze the stationary spatial distribution of a node moving according to the RWP model in a given convex area. For this, we give an explicit expression, which is in the form of a one-dimensional integral giving the density up to a normalization constant. This result is also generalized to the case where the waypoints have a nonuniform distribution. As a special case, we study a modified RWP model, where the waypoints are on the perimeter. The analytical results are illustrated through numerical examples. Moreover, the analytical results are applied to study certain performance aspects of ad hoc networks, namely, connectivity and traffic load distribution.
TL;DR: Distributed algorithms to compute an optimal routing scheme that maximizes the time at which the first node in the network drains out of energy are proposed.
Abstract: A sensor network of nodes with wireless transceiver capabilities and limited energy is considered. We propose distributed algorithms to compute an optimal routing scheme that maximizes the time at which the first node in the network drains out of energy. The problem is formulated as a linear programming problem and subgradient algorithms are used to solve it in a distributed manner. The resulting algorithms have low computational complexity and are guaranteed to converge to an optimal routing scheme that maximizes the network lifetime. The algorithms are illustrated by an example in which an optimal flow is computed for a network of randomly distributed nodes. We also show how our approach can be used to obtain distributed algorithms for many different extensions to the problem. Finally, we extend our problem formulation to more general definitions of network lifetime to model realistic scenarios in sensor networks
TL;DR: This work presents a robust and lightweight solution for sybil attack problem based on received signal strength indicator (RSSI) readings of messages and shows that even though RSSI is time-varying and unreliable in general and radio transmission is non-isotropic, it is feasible to overcome these problems.
Abstract: A sybil node impersonates other nodes by broadcasting messages with multiple node identifiers (ID). In contrast to existing solutions which are based on sharing encryption keys, we present a robust and lightweight solution for sybil attack problem based on received signal strength indicator (RSSI) readings of messages. Our solution is robust since it detects all sybil attack cases with 100% completeness and less than a few percent false positives. Our solution is lightweight in the sense that alongside the receiver we need the collaboration of one other node (i.e., only one message communication) for our protocol. We show through experiments that even though RSSI is time-varying and unreliable in general and radio transmission is non-isotropic, using ratio of RSSIs from multiple receivers it is feasible to overcome these problems.
TL;DR: In this article, the scaling laws of the information theoretic capacity of the network were identified in the case of dense networks, where the area is fixed and the density of nodes increasing.
Abstract: n source and destination pairs randomly located in an area want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power loss of r^{-alpha}, as well as a random phase. We identify the scaling laws of the information theoretic capacity of the network. In the case of dense networks, where the area is fixed and the density of nodes increasing, we show that the total capacity of the network scales linearly with n. This improves on the best known achievability result of n^{2/3} of Aeron and Saligrama, 2006. In the case of extended networks, where the density of nodes is fixed and the area increasing linearly with n, we show that this capacity scales as n^{2-alpha/2} for 2 3. The best known earlier result (Xie and Kumar 2006) identified the scaling law for alpha > 4. Thus, much better scaling than multihop can be achieved in dense networks, as well as in extended networks with low attenuation. The performance gain is achieved by intelligent node cooperation and distributed MIMO communication. The key ingredient is a hierarchical and digital architecture for nodal exchange of information for realizing the cooperation.
TL;DR: A class of weighted gradient methods for distributed resource allocation over a network is considered and sufficient conditions on the edge weights for the algorithm to converge monotonically to the optimal solution have the form of a linear matrix inequality.
Abstract: We consider a class of weighted gradient methods for distributed resource allocation over a network. Each node of the network is associated with a local variable and a convex cost function; the sum of the variables (resources) across the network is fixed. Starting with a feasible allocation, each node updates its local variable in proportion to the differences between the marginal costs of itself and its neighbors. We focus on how to choose the proportional weights on the edges (scaling factors for the gradient method) to make this distributed algorithm converge and on how to make the convergence as fast as possible. We give sufficient conditions on the edge weights for the algorithm to converge monotonically to the optimal solution; these conditions have the form of a linear matrix inequality. We give some simple, explicit methods to choose the weights that satisfy these conditions. We derive a guaranteed convergence rate for the algorithm and find the weights that minimize this rate by solving a semidefinite program. Finally, we extend the main results to problems with general equality constraints and problems with block separable objective function.
TL;DR: In this article, a network for power transmission to a receiver that converts the power into current includes a first node for transmitting power wirelessly in a first area, and the second area has a minimum electric or magnetic field strength and overlaps the first area to define an overlap area.
Abstract: A network for power transmission to a receiver that converts the power into current includes a first node for transmitting power wirelessly in a first area. The first area has a minimum electric or magnetic field strength. The network includes a second node for transmitting power wirelessly in a second area. The second area has a minimum electric or magnetic field strength and overlaps the first area to define an overlap area. In another embodiment, the network includes a source in communication with the first and second nodes which provides power to them. Also disclosed are methods for power transmission to a receiver that converts the power into current.
TL;DR: A suite of location-based compromise-tolerant security mechanisms, based on a new cryptographic concept called pairing, by binding private keys of individual nodes to both their IDs and geographic locations, and an LBK-based neighborhood authentication scheme to localize the impact of compromised nodes to their vicinity are proposed.
Abstract: Node compromise is a serious threat to wireless sensor networks deployed in unattended and hostile environments. To mitigate the impact of compromised nodes, we propose a suite of location-based compromise-tolerant security mechanisms. Based on a new cryptographic concept called pairing, we propose the notion of location-based keys (LBKs) by binding private keys of individual nodes to both their IDs and geographic locations. We then develop an LBK-based neighborhood authentication scheme to localize the impact of compromised nodes to their vicinity. We also present efficient approaches to establish a shared key between any two network nodes. In contrast to previous key establishment solutions, our approaches feature nearly perfect resilience to node compromise, low communication and computation overhead, low memory requirements, and high network scalability. Moreover, we demonstrate the efficacy of LBKs in counteracting several notorious attacks against sensor networks such as the Sybil attack, the identity replication attack, and wormhole and sinkhole attacks. Finally, we propose a location-based threshold-endorsement scheme, called LTE, to thwart the infamous bogus data injection attack, in which adversaries inject lots of bogus data into the network. The utility of LTE in achieving remarkable energy savings is validated by detailed performance evaluation.
TL;DR: A novel MAC layer relay-enabled distributed coordination function (DCF) protocol, called rDCF, is proposed to further exploit the physical layer multirate capability of IEEE 802.11 and can significantly reduce the packet delay, improve the system throughput, and alleviate the impact of channel errors on fairness.
Abstract: It is well known that IEEE 802.11 provides a physical layer multirate capability and, hence, MAC layer mechanisms are needed to exploit this capability. Several solutions have been proposed to achieve this goal. However, these solutions only consider how to exploit good channel quality for the direct link between the sender and the receiver. Since IEEE 802.11 supports multiple transmission rates in response to different channel conditions, data packets may be delivered faster through a relay node than through the direct link if the direct link has low quality and low rate. In this paper, we propose a novel MAC layer relay-enabled distributed coordination function (DCF) protocol, called rDCF, to further exploit the physical layer multirate capability. We design a protocol to assist the sender, the relay node, and the receiver to reach an agreement on which data rate to use and whether to transmit the data through a relay node. Considering various issues, such as, bandwidth utilization, channel errors, and security, we propose techniques to further improve the performance of rDCF. Simulation results show that rDCF can significantly reduce the packet delay, improve the system throughput, and alleviate the impact of channel errors on fairness
TL;DR: Two novel methods which can develop optimizing Top-Hat morphological filtering parameters are presented for spot target detection, one based on neural network and the other based on genetic algorithm.
TL;DR: This paper develops a method for mapping a virtual network onto a substrate network in a cost-efficient way, while allocating sufficient capacity to virtual network links to ensure that the virtual network can handle any traffic pattern allowed by a general set of traffic constraints.
Abstract: Virtualization has been proposed as a vehicle for overcoming the growing problem of internet ossification [1]. This paper studies the problem of mapping diverse virtual networks onto a common physical substrate. In particular, we develop a method for mapping a virtual network onto a substrate network in a cost-efficient way, while allocating sufficient capacity to virtual network links to ensure that the virtual network can handle any traffic pattern allowed by a general set of traffic constraints. Our approach attempts to find the best topology in a family of backbone-star topologies, in which a subset of nodes constitute the backbone, and the remaining nodes each connect to the nearest backbone node. We investigate the relative cost-effectiveness of different backbone topologies on different substrate networks, under a wide range of traffic conditions. Specifically, we study how the most cost-effective topology changes as the tightness of pairwise traffic constraints and the constraints on traffic locality are varied. In general, we find that as pairwise traffic constraints are relaxed, the least-cost backbone topology becomes increasingly “tree-like”. We also find that the cost of the constructed virtual networks is usually no more than 1.5 times a computed lower bound on the network cost and that the quality of solutions improves as the traffic locality gets weaker.
TL;DR: It is shown that for a cellular system employing orthogonal frequency-division multiple-access (OFDMA), the optimization of physical layer transmission strategies can be done efficiently by introducing a set of pricing variables.
Abstract: This paper considers a wireless cooperative cellular data network with a base station and many subscribers in which the subscribers have the ability to relay information for each other to improve the overall network performance. For a wireless network operating in a frequency-selective fading environment, the choices of relay node, relay strategy, and the allocation of power and bandwidth for each user are important design parameters. The design challenge is compounded further by the need to take user traffic demands into consideration. This paper proposes a utility maximization framework for such a network. We show that for a cellular system employing orthogonal frequency-division multiple-access (OFDMA), the optimization of physical layer transmission strategies can be done efficiently by introducing a set of pricing variables. The proposed solution incorporates both user traffic demand and the physical channel realization in a cross-layer design that not only allocates power and bandwidth optimally for each user, but also selects the best relay node and best relay strategy (i.e, decode-and-forward vs. amplify-and-forward) for each source-destination pair.
TL;DR: In this article, a method of operating a voice-enabled business directory search system includes receiving category-business pairs, each category business pair including a business category and a specific business, and establishing a data structure having nodes based on the category business pairs Each node of the data structure is associated with one or more business categories and a speech recognition language model for recognizing specific businesses associated with the one or multiple businesses categories.
Abstract: A method of operating a voice-enabled business directory search system includes receiving category-business pairs, each category-business pair including a business category and a specific business, and establishing a data structure having nodes based on the category-business pairs Each node of the data structure is associated with one or more business categories and a speech recognition language model for recognizing specific businesses associated with the one or more businesses categories
TL;DR: This project evaluates different physical attacks against sensor node hardware and details about the effort needed for physical attacks allows to fine tune security protocols in WSNs so they provide optimal protection at minimal cost.
Abstract: Most security protocols for wireless sensor networks (WSN) assume that the adversary can gain full control over a sensor node through direct physical access (node capture attack). But so far the amount of effort an attacker has to undertake in a node capture attack is unknown. In our project we evaluate different physical attacks against sensor node hardware. Detailed knowledge about the effort needed for physical attacks allows to fine tune security protocols in WSNs so they provide optimal protection at minimal cost.
TL;DR: In this paper, the authors describe a method for constructing a self-configuring ad-hoc network using a GPS coordinate from a WWAN channel node at a management system and creating an initial topography based at least in part on the GPS coordinate.
Abstract: Embodiments describe registration in a wireless communication system. A method includes wirelessly transmitting over a WWAN a first registration message from a mobile device, wirelessly transmitting through the WWAN a second registration message to a WLAN access point and receiving at the mobile device access through the WLAN access point. According to another embodiment is a method for constructing a self-configuring ad-hoc network. The method can include receiving a GPS coordinate from a WWAN channel node at a management system and creating an initial topography based at least in part on the GPS coordinate to achieve a network connectivity with diverse routes between a plurality of nodes.
TL;DR: It is shown that existing STBCs designed for N/sub c/ /spl ges/ 2 co-located antennas are favorable choices for the code matrix guaranteeing a diversity order of d = min{N/sub S/, N/ sub c/} if n/ sub S/ nodes are active.
Abstract: In this paper, a new class of distributed space-time block codes (DSTBCs) is introduced. These DSTBCs are designed for wireless networks which have a large set of single-antenna relay nodes Nscr, but at any given time only a small, a priori unknown subset of nodes SsubeNscr can be active. In the proposed scheme, the signal transmitted by an active relay node is the product of an information-carrying code matrix and a unique node signature vector of length Nc. It is shown that existing STBCs designed for Nc2 co-located antennas are favorable choices for the code matrix, guaranteeing a diversity order of d=min{NS,Nc} if NS nodes are active. For the most interesting case, NSgesNc, the performance loss entailed by the distributed implementation is analytically characterized. Furthermore, efficient methods for the optimization of the set of signature vectors are provided. Depending on the chosen design, the proposed DSTBCs allow for low-complexity coherent, differential, and noncoherent detection, respectively. Possible applications include ad hoc and sensor networks employing decode-and-forward relaying
TL;DR: The results indicate that the use of the Voronoi tessellation of 3D space to create truncated octahedral cells results in the best strategy for node placement, and the approach and results presented in this paper could be used for extending the processes of 2D network design to 3D networks.
Abstract: Although most wireless terrestrial networks are based on two-dimensional (2D) design, in reality, such networks operate in three-dimensions (3D). Since most often the size (i.e., the length and the width) of such terrestrial networks is significantly larger than the differences in the third dimension (i.e., the height) of the nodes, the 2D assumption is somewhat justified and usually it does not lead to major inaccuracies. However, in some environments, this is not the case; the underwater, atmospheric, or space communications being such apparent examples. In fact, recent interest in underwater acoustic ad hoc and sensor networks hints at the need to understand how to design networks in 3D. Unfortunately, the design of 3D networks is surprisingly more difficult than the design of 2D networks. For example, proofs of Kelvin's conjecture and Kepler's conjecture required centuries of research to achieve breakthroughs, whereas their 2D counterparts are trivial to solve. In this paper, we consider the coverage and connectivity issues of 3D networks, where the goal is to find a node placement strategy with 100% sensing coverage of a 3D space, while minimizing the number of nodes required for surveillance. Our results indicate that the use of the Voronoi tessellation of 3D space to create truncated octahedral cells results in the best strategy. In this truncated octahedron placement strategy, the transmission range must be at least 1.7889 times the sensing range in order to maintain connectivity among nodes. If the transmission range is between 1.4142 and 1.7889 times the sensing range, then a hexagonal prism placement strategy or a rhombic dodecahedron placement strategy should be used. Although the required number of nodes in the hexagonal prism and the rhombic dodecahedron placement strategies is the same, this number is 43.25% higher than the number of nodes required by the truncated octahedron placement strategy. We verify by simulation that our placement strategies indeed guarantee ubiquitous coverage. We believe that our approach and our results presented in this paper could be used for extending the processes of 2D network design to 3D networks.
TL;DR: This article addresses the problem of counting the number of peers in a peer-to-peer system and more generally of aggregating statistics of individual peers over the whole system, and proposes two generic techniques to solve this problem.
Abstract: In this article we address the problem of counting the number of peers in a peer-to-peer system, and more generally of aggregating statistics of individual peers over the whole system. This functionality is useful in many applications, but hard to achieve when each node has only a limited, local knowledge of the whole system. We propose two generic techniques to solve this problem. The Random Tour method is based on the return time of a continuous time random walk to the node originating the query. The Sample and Collide method is based on counting the number of random samples gathered until a target number of redundant samples are obtained. It is inspired by the "birthday paradox" technique of [6], upon which it improves by achieving a target variance with fewer samples. The latter method relies on a sampling sub-routine which returns randomly chosen peers. Such a sampling algorithm is of independent interest. It can be used, for instance, for neighbour selection by new nodes joining the system. We use a continuous time random walk to obtain such samples. We analyse the complexity and accuracy of the two methods. We illustrate in particular how expansion properties of the overlay affect their performance.