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37
Organizing a Global Coordinate System from Local Information on an Amorphous Computer
, 1999
"... This paper demonstrates that it is possible to generate a reasonably accurate coordinate system on randomly distributed processors, using only local information and local communication. By coordinate system we imply that each element assigns itself a logical coordinate that maps to its global phy ..."
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Cited by 261 (5 self)
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This paper demonstrates that it is possible to generate a reasonably accurate coordinate system on randomly distributed processors, using only local information and local communication. By coordinate system we imply that each element assigns itself a logical coordinate that maps to its global physical location, starting with no apriori knowledge of position or orientation. The algorithm presented is inspired by biological systems that use chemical gradients to determine the position of cells [12]. Extensive analysis and simulation results are presented. Two key results are: there is a critical minimum average neighborhood size of 15 for good accuracy and there is a fundamental limit on the resolution of any coordinate system determined strictly from local communication. We also demonstrate that using this algorithm, random distributions of processors produce significantly better accuracy than regular processor grids  such as those used by cellular automata. This has implications for discrete models of biology as well as for building smart sensor arrays.
Connectivity in AdHoc and Hybrid Networks
 IN PROC. IEEE INFOCOM
, 2002
"... We consider a largescale wireless network, but with a low density of nodes per unit area. Interferences are then less critical, contrary to connectivity. This paper studies the latter property for both a purely adhoc network and a hybrid network, where fixed base stations can be reached in multipl ..."
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Cited by 160 (6 self)
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We consider a largescale wireless network, but with a low density of nodes per unit area. Interferences are then less critical, contrary to connectivity. This paper studies the latter property for both a purely adhoc network and a hybrid network, where fixed base stations can be reached in multiple hops. We assume here that power constraints are modeled by a maximal distance above which two nodes are not (directly) connected. We find that
Investigating upper bounds on network lifetime extension for cellbased energy conservation techniques in stationary ad hoc networks
 in Proceedings of the ACM/IEEE International COnference on Mobile Computing and Networking (MOBICOM
, 2002
"... Cooperative cellbased strategies have been recently proposed as a technique for extending the lifetime of wireless ad hoc networks, while only slightly impacting network performance. The effectiveness of this approach depends heavily on the node density: the higher it is, the more consistent energy ..."
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Cited by 103 (5 self)
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Cooperative cellbased strategies have been recently proposed as a technique for extending the lifetime of wireless ad hoc networks, while only slightly impacting network performance. The effectiveness of this approach depends heavily on the node density: the higher it is, the more consistent energy savings can potentially be achieved. However, no general analyses of network lifetime have been done either for a base network (one without any energy conservation technique) or for one using cooperative energy conservation strategies. In this paper, we investigate the lifetime/density tradeoff under the hypothesis that nodes are distributed uniformly at random in a given region, and that the traffic is evenly distributed across the network. We also analyze the case where the node density is just sufficient to ensure that the network is connected with high probability. This analysis, which is supported by the results of extensive simulations, shows that even in this low density scenario, cellbased strategies can significantly extend network lifetime.
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks
, 2003
"... In this paper, we analyze the critical transmitting range for connectivity in wireless ad hoc networks. More specifically, we consider the following problem: assume n nodes, each capable of communicating with nodes within a radius of r, are randomly and uniformly distributed in a ddimensional re ..."
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Cited by 102 (12 self)
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In this paper, we analyze the critical transmitting range for connectivity in wireless ad hoc networks. More specifically, we consider the following problem: assume n nodes, each capable of communicating with nodes within a radius of r, are randomly and uniformly distributed in a ddimensional region with a side of length l; how large must the transmitting range r be to ensure that the resulting network is connected with high probability? First, we consider this problem for stationary networks, and we provide tight upper and lower bounds on the critical transmitting range for onedimensional networks, and nontight bounds for two and threedimensional networks. Due to the presence of the geometric parameter l in the model, our results can be applied to dense as well as sparse ad hoc networks, contrary to existing theoretical results that apply only to dense networks. We also investigate several related questions through extensive simulations. First, we evaluate the relationship between the critical transmitting range and the minimum transmitting range that ensures formation of a connected component containing a large fraction (e.g. 90%) of the nodes. Then, we consider the mobile version of the
Error Characteristics of Ad Hoc Positioning Systems (APS)
, 2004
"... APS algorithms use the basic idea of distance vector routing to find positions in an ad hoc network using only a fraction of landmarks, for example GPS enabled nodes. All the nodes in the network are assumed to have the possibility of measuring: range, angle of arrival (AOA), orientation, or a combi ..."
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Cited by 63 (0 self)
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APS algorithms use the basic idea of distance vector routing to find positions in an ad hoc network using only a fraction of landmarks, for example GPS enabled nodes. All the nodes in the network are assumed to have the possibility of measuring: range, angle of arrival (AOA), orientation, or a combination of them. We give a lower bound for positioning error in a multihop network for a range/angle free algorithm, and examine the error characteristics of four classes of multihop APS algorithms under various conditions, using theoretical analysis and simulations. Analysis of range/angle free, range based, angle based, and multimodal algorithms shows a complex tradeo# between the capabilities used, the density of the network, ratio of landmarks, and the quality of the positions obtained.
On The Symmetric Range Assignment Problem In Wireless Ad Hoc Networks
, 2002
"... In this paper we consider a constrained version of the range assignment problem for wireless ad hoc networks, where the value the node transmitting ranges must be assigned in such a way that the resulting communication graph is strongly connected and the energy cost is minimum. We impose the further ..."
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Cited by 37 (1 self)
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In this paper we consider a constrained version of the range assignment problem for wireless ad hoc networks, where the value the node transmitting ranges must be assigned in such a way that the resulting communication graph is strongly connected and the energy cost is minimum. We impose the further requirement of symmetry on the resulting communication graph. We also consider a weaker notion of symmetry, in which only the existence of a set of symmetric edges that renders the communication graph connected is required. Our interest in these problems is motivated by the fact that a (weakly) symmetric range assignment can be more easily integrated with existing higher and lowerlevel protocols for ad hoc networks, which assume that all the nodes have the same transmitting range. We show that imposing symmetry does not change the complexity of the problem, which remains NPhard in two and threedimensional networks. We also show that a weakly symmetric range assignment can reduce the energy cost considerably with respect to the homogeneous case, in which all the nodes have the same transmitting range, and that no further (asymptotic) bene t is expected from the asymmetric range assignment. Hence, the results presented in this paper indicate that weak symmetry is a desirable property of the range assignment.
The BinCovering Technique for Thresholding Random Geometric Graph Properties
, 2005
"... We study the emerging phenomenon of ad hoc, sensorbased communication networks. The communication is modeled by the random geometric graph model G(n, r, ℓ) where n points randomly placed within [0, ℓ] d form the nodes, and any two nodes that correspond to points at most distance r away from each ot ..."
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Cited by 34 (3 self)
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We study the emerging phenomenon of ad hoc, sensorbased communication networks. The communication is modeled by the random geometric graph model G(n, r, ℓ) where n points randomly placed within [0, ℓ] d form the nodes, and any two nodes that correspond to points at most distance r away from each other are connected. We study fundamental properties of G(n, r, ℓ) of interest: connectivity, coverage, and routingstretch. Our main contribution is a simple analysis technique we call bincovering that we apply uniformly to get (asymptotically) tight thresholds for each of these properties. Typically, in the past, random geometric graph analyses involved sophisticated methods from continuum percolation theory; on contrast, our bincovering approach is discrete and very simple, yet it gives us tight threshold bounds. The technique also yields algorithmic benefits as illustrated by a simple local routing algorithm for finding paths with low stretch. Our specific results should also prove interesting to the networking community that has seen a recent increase in the study of random geometric graphs motivated by engineering ad hoc networks.
Continuum percolation with unreliable and spread out connections
 Journal of Statistical Physics
, 2005
"... We derive percolation results in the continuum plane that lead to what appears to be a general tendency of many stochastic network models. Namely, when the selection mechanism according to which nodes are connected to each other, is sufficiently spread out, then a lower density of nodes, or on avera ..."
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Cited by 31 (2 self)
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We derive percolation results in the continuum plane that lead to what appears to be a general tendency of many stochastic network models. Namely, when the selection mechanism according to which nodes are connected to each other, is sufficiently spread out, then a lower density of nodes, or on average fewer connections per node, are sufficient to obtain an unbounded connected component. We look at two different transformations that spread out connections and decrease the critical percolation density while preserving the average node degree. Our results indicate that real networks can exploit the presence of spreadout and unreliable connections to achieve connectivity more easily, provided they can maintain the average number of functioning connections per node.
A Statistical Analysis of the LongRun Node Spatial Distribution in Mobile Ad Hoc Networks
, 2002
"... In this paper, we analyze the node spatial distribution of a mobile wireless ad hoc networks. Characterizing this distribution is of fundamental importance in the analysis of many relevant properties of mobile ad hoc networks, such as connectivity, average route length, and network capacity. In part ..."
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Cited by 27 (3 self)
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In this paper, we analyze the node spatial distribution of a mobile wireless ad hoc networks. Characterizing this distribution is of fundamental importance in the analysis of many relevant properties of mobile ad hoc networks, such as connectivity, average route length, and network capacity. In particular, we have investigated under what conditions the node spatial distribution resulting after a large number of mobility steps resembles the uniform distribution. This is motivated by the fact that the existing theoretical results concerning mobile ad hoc networks are based on this assumption. In order to test this hypothesis, we performed extensive simulations using two wellknown mobility models: the random waypoint model, which resembles intentional movement, and a Brownianlike model, which resembles nonintentional movement. Our analysis has shown that in the Brownianlike motion the uniformity assumption does hold, and that the intensity of the concentration of nodes in the center of the deployment region that occurs in the random waypoint model heavily depends on the choice of some mobility parameters. For extreme values of these parameters, the uniformity assumption is impaired.
An Evaluation of Connectivity in Mobile Wireless Ad Hoc Networks
 DSN'02
, 2002
"... We consider the following problem for wireless ad hoc networks: assume n nodes, each capable of communicating with nodes within a radius of r, are distributed in a ddimensional region of side l; how large must the transmitting range r be to ensure that the resulting network is connected? We also con ..."
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Cited by 26 (4 self)
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We consider the following problem for wireless ad hoc networks: assume n nodes, each capable of communicating with nodes within a radius of r, are distributed in a ddimensional region of side l; how large must the transmitting range r be to ensure that the resulting network is connected? We also consider the mobile version of the problem, in which nodes are allowed to move during a time interval and the value of r ensuring connectedness for a given fraction of the interval must be determined. For the stationary case, we give tight bounds on the relative magnitude of r, n and l yielding a connected graph with high probability in 1dimensional networks, thus solving an open problem. The mobile version of the problem when d=2 is investigated through extensive simulations, which give insight on how mobility affect connectivity and reveal a useful tradeoff between communication capability and energy consumption.