### Browsing by Author "Han, Guang"

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Item Connectivity analysis of wireless ad-hoc networks(2007-08-27) Han, Guang; Makowski, Armand; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Connectivity is one of the most fundamental properties of wireless ad-hoc networks as most network functions are predicated upon the network being connected. Although increasing node transmission power will improve network connectivity, too large a power level is not feasible as energy is a scarce resource in wireless ad-hoc networks. Thus, it is crucial to identify the minimum node transmission power that will ensure network connectivity with high probability. It is known that there exists a critical level transmission power such that a suitably larger power will ensure network connectivity with high probability. A small variation across this threshold level will lead to a sharp transition of the probability that the network is connected. Thus, in order to precisely estimate the minimum node transmission power, not only do we need to identify this critical threshold, but also how fast this transition takes place. To characterize the sharpness of transition, we define weak, strong and very strong critical thresholds associated with increasing transition speeds. In this dissertation, we seek to estimate the minimum node transmission power for large scale one-dimensional wireless ad-hoc networks under the Geometric Random Graph (GRG) models. Unlike in previous works where nodes are taken to be uniformly distributed, we assume a more general node distribution. Using the methods of first and second moments, we theoretically prove the existence of a very strong critical threshold when the density function is everywhere positive. On the other hand, only weak thresholds are shown to exist when the density function contains vanishing densities. We also study the connectivity of two-dimensional wireless ad-hoc networks under the random connection model, which accounts for statistical channel variations. With the help of the Stein-Chen method, we derive a closed form formula for the limiting probability that there are no isolated nodes under a very general assumption of channel variations. The node transmission power to ensure the absence of isolated nodes provides a tight lower bound on the transmission power needed to ensure network connectivity.Item Connectivity in one-dimensional geometric random graphs: Poisson approximations, zero-one laws and phase transitions(2008-10-24) Han, Guang; Makowski, Armand M.; Makowski, Armand M.Consider n points (or nodes) distributed uniformly and independently on the unit interval [0,1]. Two nodes are said to be adjacent if their distance is less than some given threshold value.For the underlying random graph we derive zero-one laws for the property of graph connectivity and give the asymptotics of the transition widths for the associated phase transition. These results all flow from a single convergence statement for the probability of graph connectivity under a particular class of scalings. Given the importance of this result, we give two separate proofs; one approach relies on results concerning maximal spacings, while the other one exploits a Poisson convergence result for the number of breakpoint users.Item A New Approach towards Solving the Location Discovery Problem in Wireless Sensor Networks(2003-12-19) Han, Guang; Hua, Shaoxiong; Qu, GangLocation discovery in wireless sensor network (WSN) is the process that sensor nodes collaborate to determine the position for unknown sensor nodes. Anchors, sensors that know their locations, are expensive but are required to be deployed into the WSN to solve this problem. Thus it is desirable to minimize the number of anchors for this purpose. In this paper, we propose an anchor deployment scheme and a novel bilateration locationing algorithm to achieve this goal. The basic idea of anchor deployment method is to have three anchors deployed as a group, and locate sensors around them expansively. The novelty of our bilateration algorithm is that it in general requires only two neighbor sensors to determine a node's location. Comparing with the state-of-the-art location discovery approaches, our algorithm gives location estimation with high accuracy, low communication cost and very small anchor percentage. We conduct theoretical analysis about location estimation error and extensive simulation shows that our algorithm can derive sensor location within 4% location error and much less communication cost compared with other algorithms. UMIACS-TR-2003-119Item On the critical communication range under node placement with vanishing densities(2007) Han, Guang; Makowski, Armand M.; Makowski, Armand M.; ISRWe consider the random network where n points are placed independently on the unit interval [0, 1] according to some probability distribution function F. Two nodes communicate with each other if their distance is less than some transmission range. When F admits a continuous density f with f = inf (f(x), x [0, 1]) > 0, it is known that the property of graph connectivity for the underlying random graph admits a strong critical threshold. Through a counterexample, we show that only a weak critical threshold exists when f = 0 and we identify it. Implications for the critical transmission range are discussed.Item On zero-one laws for connectivity in one-dimensional geometric random graphs(2006) Han, Guang; Makowski, Armand M.; Makowski; ISR; CSHCNWe consider the geometric random graph where n points are distributed uniformly and independently on the unit interval [0,1]. Using the method of first and second moments, we provide a simple proof of the "zero-one" law for the property of graph connectivity under the asymptotic regime created by having n become large and the transmission range scaled appropriately with n.Item A strong zero-one law for connectivity in one-dimensional geometric random graphs with non-vanishing densities(2007) Han, Guang; Makowski, Armand M.; Makowski, Armand M.; ISRWe consider the geometric random graph where n points are distributed independently on the unit interval [0,1] according to some probability distribution function F. Two nodes communicate with each other if their distance is less than some transmission range. When F admits a continuous density f which is strictly positive on [0,1], we show that the property of graph connectivity exhibits a strong critical threshold and we identify it. This is achieved by generalizing a limit result on maximal spacings due to Levy for the uniform distribution.Item Very sharp transitions in one-dimensional MANETs(2005) Han, Guang; Makowski, Armand M.; Makowski, Armand M.; ISR; CSHCNWe investigate how quickly phase transitions can occur in one-dimensional geometric random graph models of MANETs. In the case of graph connectivity, we show that the transition width behaves like 1/n (when the number n of users is large), a significant improvement over general asymptotic bounds given recently by Goel et al. for monotone graph properties. We also discuss a similar result for the property that there exists no isolated user in the network. The asymptotic results are validated by numerical computations. Finally we outline how the approach sed here could be applied in higher dimensions and or other graph properties.