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33
Securing localization with hidden and mobile base stations
 In IEEE Conference on Computer Communications (INFOCOM
, 2006
"... Abstract — Until recently, the problem of localization in wireless networks has been mainly studied in a nonadversarial setting. Only recently, a number of solutions have been proposed that aim to detect and prevent attacks on localization systems. In this work, we propose a new approach to secure ..."
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Cited by 43 (4 self)
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Abstract — Until recently, the problem of localization in wireless networks has been mainly studied in a nonadversarial setting. Only recently, a number of solutions have been proposed that aim to detect and prevent attacks on localization systems. In this work, we propose a new approach to secure localization based on hidden and mobile base stations. Our approach enables secure localization with a broad spectrum of localization techniques: ultrasonic or radio, based on received signal strength or signal time of flight. Through several examples we show how this approach can be used to secure nodecentric and infrastructurecentric localization schemes. We further show how this approach can be applied to secure localization in sensor networks. I.
On the cover time and mixing time of random geometric graphs
 Theor. Comput. Sci
, 2007
"... The cover time and mixing time of graphs has much relevance to algorithmic applications and has been extensively investigated. Recently, with the advent of adhoc and sensor networks, an interesting class of random graphs, namely random geometric graphs, has gained new relevance and its properties ..."
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Cited by 26 (2 self)
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The cover time and mixing time of graphs has much relevance to algorithmic applications and has been extensively investigated. Recently, with the advent of adhoc and sensor networks, an interesting class of random graphs, namely random geometric graphs, has gained new relevance and its properties have been the subject of much study. A random geometric graph G(n, r) is obtained by placing n points uniformly at random on the unit square and connecting two points iff their Euclidean distance is at most r. The phase transition behavior with respect to the radius r of such graphs has been of special interest. We show that there exists a critical radius ropt such that for any r ≥ ropt G(n, r) has optimal cover time of Θ(n log n) with high probability, and, importantly, ropt = Θ(rcon) where rcon denotes the critical radius guaranteeing asymptotic connectivity. Moreover, since a disconnected graph has infinite cover time, there is a phase transition and the corresponding threshold width is O(rcon). On the other hand, the radius required for rapid mixing rrapid = ω(rcon), and, in particular, rrapid = Θ(1/poly(log n)). We are able to draw our results by giving a tight bound on the electrical resistance and conductance of G(n, r) via certain constructed flows.
Many Random Walks Are Faster Than One
"... We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the cover time–the expected time required to visit every node in a ..."
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Cited by 21 (3 self)
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We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the cover time–the expected time required to visit every node in a graph at least once–and we show that for a large collection of interesting graphs, running many random walks in parallel yields a speedup in the cover time that is linear in the number of parallel walks. We demonstrate that an exponential speedup is sometimes possible, but that some natural graphs allow only a logarithmic speedup. A problem related to ours (in which the walks start from some probabilistic distribution on vertices) was previously studied in the context of space efficient algorithms for undirected stconnectivity and our results yield, in certain cases, an improvement upon some of the earlier bounds.
On the Cover Time of Random Geometric Graphs
 In: ICALP. (2005
, 2005
"... Abstract. The cover time of graphs has much relevance to algorithmic applications and has been extensively investigated. Recently, with the advent of adhoc and sensor networks, an interesting class of random graphs, namely random geometric graphs, has gained new relevance and its properties have be ..."
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Cited by 17 (4 self)
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Abstract. The cover time of graphs has much relevance to algorithmic applications and has been extensively investigated. Recently, with the advent of adhoc and sensor networks, an interesting class of random graphs, namely random geometric graphs, has gained new relevance and its properties have been the subject of much study. A random geometric graph G(n, r) is obtained by placing n points uniformly at random on the unit square and connecting two points iff their Euclidean distance is at most r. The phase transition behavior with respect to the radius r of such graphs has been of special interest. We show that there exists a critical radius ropt such that for any r ≥ ropt G(n, r) has optimal cover time of Θ(n log n) with high probability, and, importantly, ropt = Θ(rcon) where rcon denotes the critical radius guaranteeing asymptotic connectivity. Moreover, since a disconnected graph has infinite cover time, there is a phase transition and the corresponding threshold width is O(rcon). We are able to draw our results by giving a tight bound on the electrical resistance of G(n, r) via the power of certain constructed flows. 1
How to Explore a FastChanging World (Cover Time of a Simple Random Walk on Evolving Graphs)
"... Abstract. Motivated by real world networks and use of algorithms based on random walks on these networks we study the simple random walks on dynamic undirected graphs with fixed underlying vertex set, i.e., graphs which are modified by inserting or deleting edges at every step of the walk. We are in ..."
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Cited by 16 (0 self)
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Abstract. Motivated by real world networks and use of algorithms based on random walks on these networks we study the simple random walks on dynamic undirected graphs with fixed underlying vertex set, i.e., graphs which are modified by inserting or deleting edges at every step of the walk. We are interested in the expected time needed to visit all the vertices of such a dynamic graph, the cover time, under the assumption that the graph is being modified by an oblivious adversary. It is well known that on connected static undirected graphs the cover time is polynomial in the size of the graph. On the contrary and somewhat counterintuitively, we show that there are adversary strategies which force the expected cover time of a simple random walk on connected dynamic graphs to be exponential. We relate this result to the cover time of static directed graphs. In addition we provide a simple strategy, the lazy random walk, that guarantees polynomial cover time regardless of the changes made by the adversary. 1
Bounds on the Mixing Time and Partial Cover of AdHoc and Sensor Networks
, 2004
"... In [1], the authors proposed the partial cover of a random walk on a broadcast network to be used to gather information and supported their proposal with experimental results. In this paper, we demonstrate analytically that for sufficiently large broadcast radius, the partial cover of a random walk ..."
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Cited by 14 (3 self)
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In [1], the authors proposed the partial cover of a random walk on a broadcast network to be used to gather information and supported their proposal with experimental results. In this paper, we demonstrate analytically that for sufficiently large broadcast radius, the partial cover of a random walk on a broadcast network is in fact efficient and generates a good distribution of the visited nodes. Our result is based on bounding the conductance, which intuitively measures the amount of bottlenecks in a graph. We show that the conductance of a random broadcast network in a unit square is #(R), and this bound allows us to analyze properties of the random walk such as mixing time and load balancing. We find that for the random walk to be both efficient and have a high quality cover and partial cover (i.e. rapid mixing), radius R = O(1/poly(logN)) is sufficient. Experimental results on the random unit disk graphs that resemble the conductance of the 3D grid indicate that the analytical bounds on efficiency, namely cover time and partial cover time, are not tight. In particular, R = O(1/N ) is sufficient radius to obtain optimal cover time and partial cover time, if one is not concerned about the quality of the distribution of the visited nodes (for example in a query based on majority vote).
The Power of Choice in Random Walks: An Empirical Study
 In MSWiM
, 2006
"... In recent years randomwalkbased algorithms have been proposed for a variety of networking tasks. These proposals include searching, routing, selfstabilization, and query processing in wireless networks, peertopeer networks and other distributed systems. This approach is gaining popularity becau ..."
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Cited by 8 (0 self)
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In recent years randomwalkbased algorithms have been proposed for a variety of networking tasks. These proposals include searching, routing, selfstabilization, and query processing in wireless networks, peertopeer networks and other distributed systems. This approach is gaining popularity because random walks present locality, simplicity, lowoverhead and inherent robustness to structural changes. In this work we propose and investigate an enhanced algorithm that we refer to as random walks with choice. In this algorithm, instead of selecting just one neighbor at each step, the walk moves to the next node after examining a small number of neighbors sampled at random. Our empirical results on random geometric graphs, the model best suited for wireless networks, suggest a significant improvement in important metrics such as the cover time and loadbalancing properties of random walks. We also systematically investigate random walks with choice on networks with a square grid topology. For this case, our simulations indicate that there is an unbounded improvement in cover time even with a choice of only two neighbors. We also observe a large reduction in the variance of the cover time, and a significant improvement in visit load balancing.
Probabilistic quorum systems in wireless ad hoc networks
 In Proceedings of the 38th IEEE International Conference on Dependable Systems and Networks (DSNDCCS
, 2008
"... Quorums are a basic construct in solving many fundamental distributed computing problems. One of the known ways of making quorums scalable and efficient is by weakening their intersection guarantee to being probabilistic. This paper explores several access strategies for implementing probabilistic q ..."
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Cited by 8 (3 self)
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Quorums are a basic construct in solving many fundamental distributed computing problems. One of the known ways of making quorums scalable and efficient is by weakening their intersection guarantee to being probabilistic. This paper explores several access strategies for implementing probabilistic quorums in ad hoc networks. In particular, we present the first detailed study of asymmetric probabilistic biquorum systems, that allow to mix different access strategies and different quorums sizes, while guaranteeing the desired intersection probability. We show the advantages of asymmetric probabilistic biquorum systems in ad hoc networks. Such an asymmetric construction is also useful for other types of networks with non uniform access costs (e.g, peertopeer networks). The paper includes both a formal analysis of these approaches backed up by an extensive simulation based study. In particular, we show that one of the strategies that uses Random Walks, exhibits the smallest communication overhead, thus being very attractive for ad hoc networks. Categories and Subject Descriptors: C.2.1 [Comp.Communication Networks]: Network Architecture and Design—Wireless communication;
Secure Location Verification with Hidden and Mobile Base Stations
"... Abstract—In this work, we propose and analyze a new approach for securing localization and location verification in wireless networks based on hidden and mobile base stations. Our approach enables secure localization with a broad spectrum of localization techniques, ultrasonic or radio, based on the ..."
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Cited by 7 (0 self)
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Abstract—In this work, we propose and analyze a new approach for securing localization and location verification in wireless networks based on hidden and mobile base stations. Our approach enables secure localization with a broad spectrum of localization techniques, ultrasonic or radio, based on the received signal strength or signal time of flight. Through several examples, we show how this approach can be used to secure nodecentric and infrastructurecentric localization schemes. We further show how this approach can be applied to secure localization in mobile ad hoc and sensor networks. Index Terms—Mobility, location verification, security, wireless networks. 1