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545
A Kernel View Of The Dimensionality Reduction Of Manifolds
, 2003
"... We interpret several wellknown algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithm ..."
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Cited by 155 (7 self)
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We interpret several wellknown algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithms can be described as kernel PCA on specially constructed Gram matrices, and illustrate the similarities and differences between the algorithms with representative examples.
Delay and Capacity Tradeoffs in Mobile Ad Hoc Networks: A Global Perspective
"... Since the original work of Grossglauser and Tse, which showed that the mobility can increase the capacity of an ad hoc network, there has been a lot of interest in characterizing the delaycapacity relationship in ad hoc networks. Various mobility models have been studied in the literature, and the ..."
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Cited by 147 (2 self)
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Since the original work of Grossglauser and Tse, which showed that the mobility can increase the capacity of an ad hoc network, there has been a lot of interest in characterizing the delaycapacity relationship in ad hoc networks. Various mobility models have been studied in the literature, and the delaycapacity relationships under those models have been characterized. The results indicate that there are tradeoffs between the delay and the capacity, and that the nature of these tradeoffs is strongly influenced by the choice of the mobility model. Some questions that arise are: (i) How representative are these mobility models studied in the lieterature? (ii) Can the delaycapacity relationship be significantly different under some other “reasonable ” mobility model? (iii) What would the delaycapacity tradeoff in a real network be like? In this paper, we address these questions. In particular, we analyze, among others, some of the mobility models that have been used in the recent related works, under a unified framework. We relate the nature of the delaycapacity tradeoff to the nature of the node motion, thereby providing a better understanding of the delaycapacity relationship in ad hoc networks than earlier works.
Singlecopy Routing in Intermittently Connected Mobile Networks
 In IEEE SECON
, 2004
"... Abstract — Intermittently connected mobile networks are wireless networks where most of the time there does not exist a complete path from source to destination, or such a path is highly unstable and may break soon after it has been discovered. In this context, conventional routing schemes would fai ..."
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Cited by 132 (11 self)
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Abstract — Intermittently connected mobile networks are wireless networks where most of the time there does not exist a complete path from source to destination, or such a path is highly unstable and may break soon after it has been discovered. In this context, conventional routing schemes would fail. To deal with such networks we propose the use of an opportunistic hopbyhop routing model. According to the model, a series of independent, local forwarding decisions are made, based on current connectivity and predictions of future connectivity information diffused through nodes’ mobility. The important issue here is how to choose an appropriate next hop. To this end, we propose and analyze via theory and simulations a number of routing algorithms. The champion algorithm turns out to be one that combines the simplicity of a simple random policy, which is efficient in finding good leads towards the destination, with the sophistication of utilitybased policies that efficiently follow good leads. We also state and analyze the performance of an oraclebased optimal algorithm, and compare it to the online approaches. The metrics used in the comparison are the average message delivery delay and the number of transmissions per message delivered. I.
Distributed Construction of Random Expander Networks
 In IEEE Infocom
, 2003
"... We present a novel distributed algorithm for constructing random overlay networks that are composed of d Hamilton cycles. The protocol is completely decentralized as no globallyknown server is required. The constructed topologies are expanders with O(log d n) diameter with high probability. ..."
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Cited by 107 (0 self)
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We present a novel distributed algorithm for constructing random overlay networks that are composed of d Hamilton cycles. The protocol is completely decentralized as no globallyknown server is required. The constructed topologies are expanders with O(log d n) diameter with high probability.
Laplacians and the Cheeger Inequality for Directed Graphs
 Annals of Combinatorics
, 2005
"... We consider Laplacians for directed graphs and examine their eigenvalues. We introduce a notion of a circulation in a directed graph and its connection with the Rayleigh quotient. We then define a Cheeger constant and establish the Cheeger inequality for directed graphs. These relations can be used ..."
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Cited by 103 (4 self)
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We consider Laplacians for directed graphs and examine their eigenvalues. We introduce a notion of a circulation in a directed graph and its connection with the Rayleigh quotient. We then define a Cheeger constant and establish the Cheeger inequality for directed graphs. These relations can be used to deal with various problems that often arise in the study of nonreversible Markov chains including bounding the rate of convergence and deriving comparison theorems. 1
An Interruptible Algorithm for Perfect Sampling via Markov Chains
 Annals of Applied Probability
, 1998
"... For a large class of examples arising in statistical physics known as attractive spin systems (e.g., the Ising model), one seeks to sample from a probability distribution # on an enormously large state space, but elementary sampling is ruled out by the infeasibility of calculating an appropriate nor ..."
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Cited by 92 (7 self)
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For a large class of examples arising in statistical physics known as attractive spin systems (e.g., the Ising model), one seeks to sample from a probability distribution # on an enormously large state space, but elementary sampling is ruled out by the infeasibility of calculating an appropriate normalizing constant. The same difficulty arises in computer science problems where one seeks to sample randomly from a large finite distributive lattice whose precise size cannot be ascertained in any reasonable amount of time. The Markov chain Monte Carlo (MCMC) approximate sampling approach to such a problem is to construct and run "for a long time" a Markov chain with longrun distribution #. But determining how long is long enough to get a good approximation can be both analytically and empirically difficult. Recently, Jim Propp and David Wilson have devised an ingenious and efficient algorithm to use the same Markov chains to produce perfect (i.e., exact) samples from #. However, the running t...
Spray and focus: Efficient mobilityassisted routing for heterogeneous and correlated mobility
 In Proceedings of IEEE PerCom Workshop on Intermittently Connected Mobile Ad Hoc Networks
, 2007
"... Intermittently connected mobile networks are wireless networks where most of the time there does not exist a complete path from the source to the destination. There are many real networks that follow this model, for example, wildlife tracking sensor networks, military networks, vehicular ad hoc netw ..."
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Cited by 79 (1 self)
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Intermittently connected mobile networks are wireless networks where most of the time there does not exist a complete path from the source to the destination. There are many real networks that follow this model, for example, wildlife tracking sensor networks, military networks, vehicular ad hoc networks (VANETs), etc. To deal with such networks researchers have suggested to use controlled replication or “spraying ” methods that can reduce the overhead of floodingbased schemes by distributing a small number of copies to only a few relays. These relays then “look” for the destination in parallel as they move into the network. Although such schemes can perform well in scenarios with high mobility (e.g. VANETs), they struggle in situations were mobility is slow and correlated in space and/or time. To route messages efficiently in such networks, we propose a scheme that also distributes a small number of copies to few relays. However, each relay can then forward its copy further using a singlecopy utilitybased scheme, instead of naively waiting to deliver it to the destination itself. This scheme exploits all the advantages of controlled replication, but is also able to identify appropriate forwarding opportunities that could deliver the message faster. Simulation results for traditional mobility models, as well as for a more realistic “communitybased ” model, indicate that our scheme can reduce the delay of existing spraying techniques up to 20 times in some scenarios. 1
Optimal ThroughputDelay Scaling in Wireless Networks  Part I: The Fluid Model
"... Gupta and Kumar (2000) introduced a random model to study throughput scaling in a wireless network with static nodes, and showed that the throughput per sourcedestination pair is Θ ( 1 / √ n log n). Grossglauser and Tse (2001) showed that when nodes are mobile it is possible to have a constant thr ..."
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Cited by 79 (2 self)
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Gupta and Kumar (2000) introduced a random model to study throughput scaling in a wireless network with static nodes, and showed that the throughput per sourcedestination pair is Θ ( 1 / √ n log n). Grossglauser and Tse (2001) showed that when nodes are mobile it is possible to have a constant throughput scaling per sourcedestination pair. In most applications delay is also a key metric of network performance. It is expected that high throughput is achieved at the cost of high delay and that one can be improved at the cost of the other. The focus of this paper is on studying this tradeoff for wireless networks in a general framework. Optimal throughputdelay scaling laws for static and mobile wireless networks are established. For static networks, it is shown that the optimal throughputdelay tradeoff is given by D(n) = Θ(nT (n)), where T (n) and D(n) are the throughput and delay scaling, respectively. For mobile networks, a simple proof of the throughput scaling of Θ(1) for the GrossglauserTse scheme is given and the associated delay scaling is shown to be Θ(n log n). The optimal throughputdelay tradeoff for mobile networks is also established. To capture physical movement in the real world, a random walk model for node mobility is assumed. It is shown that for throughput of O ( 1 / √ n log n) , which can also be achieved in static networks, the throughputdelay tradeoff is the same as in static networks, i.e., D(n) = Θ(nT (n)). Surprisingly, for almost any throughput of a higher order, the delay is shown to be Θ(n log n), which is the delay for throughput of Θ(1). Our result, thus, suggests that the use of mobility to increase throughput, even slightly, in realworld networks would necessitate an abrupt and very large increase in delay.
Vacant set of random interlacements and percolation
"... We introduce a model of random interlacements made of a countable collection of doubly infinite paths on Z d, d ≥ 3. A nonnegative parameter u measures how many trajectories enter the picture. This model describes in the large N limit the microscopic structure in the bulk, which arises when conside ..."
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Cited by 71 (16 self)
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We introduce a model of random interlacements made of a countable collection of doubly infinite paths on Z d, d ≥ 3. A nonnegative parameter u measures how many trajectories enter the picture. This model describes in the large N limit the microscopic structure in the bulk, which arises when considering the disconnection time of a discrete cylinder (Z/NZ) d−1 × Z by simple random walk, or the set of points visited by simple random walk on the discrete torus (Z/NZ) d at times of order uN d. In particular we study the percolative properties of the vacant set left by the interlacement at level u, which is an infinite connected translation invariant random subset of Z d. We introduce a critical value u ∗ such that the vacant set percolates for u < u ∗ and does not percolate for u> u∗. Our main results show that u ∗ is finite when d ≥ 3 and strictly positive when d ≥ 7.
Degenerate DelayCapacity Tradeoffs in AdHoc Networks with Brownian Mobility
 IEEE/ACM Trans. Netw
, 2006
"... Abstract — There has been significant recent interest within the networking research community to characterize the impact of mobility on the capacity and delay in mobile ad hoc networks. In this paper, we study the fundamental tradeoff between the capacity and delay for a mobile ad hoc network unde ..."
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Cited by 67 (3 self)
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Abstract — There has been significant recent interest within the networking research community to characterize the impact of mobility on the capacity and delay in mobile ad hoc networks. In this paper, we study the fundamental tradeoff between the capacity and delay for a mobile ad hoc network under the Brownian motion model. We show that the 2hop relaying scheme proposed by Grossglauser and Tse (2001), while capable of achieving Θ(1) pernode capacity, incurs an expected packet delay of Ω(log n/σ 2 n), where σ 2 n is the variance parameter of the Brownian motion model. We then show that in order to reduce the delay by any significant amount, one must be ready to accept a pernode capacity close to static ad hoc networks. In particular, we show that under a large class of scheduling and relaying schemes, if the mean packet delay is O(n α /σ 2 n), for any α < 0, then the pernode capacity must be O(1 / √ n). This result is in sharp contrast to other results that have recently been reported in the literature. I.