Results 1  10
of
13
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 ..."
Abstract

Cited by 21 (3 self)
 Add to MetaCart
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.
Fountain codes based distributed storage algorithms
, 2007
"... We consider largescale networks with n nodes, out of which k are in possession, (e.g., have sensed or collected in some other way) k information packets. In the scenarios in which network nodes are vulnerable because of, for example, limited energy or a hostile environment, it is desirable to disse ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
We consider largescale networks with n nodes, out of which k are in possession, (e.g., have sensed or collected in some other way) k information packets. In the scenarios in which network nodes are vulnerable because of, for example, limited energy or a hostile environment, it is desirable to disseminate the acquired information throughout the network so that each of the n nodes stores one (possibly coded) packet and the original k source packets can be recovered later in a computationally simple way from any (1 + ǫ)k nodes for some small ǫ> 0. We developed two distributed algorithms for solving this problem based on simple random walks and Fountain codes. Unlike all previously developed schemes, our solution is truly distributed, that is, nodes do not know n, k or connectivity in the network, except in their own neighborhoods, and they do not maintain any routing tables. In the first algorithm, all the sensors have the knowledge of n and k. In the second algorithm, each sensor estimates these parameters through the random walk dissemination. We present analysis of the communication/transmission and encoding/decoding complexity of these two algorithms, and provide extensive simulation results as well 1. 1
Fast and Efficient Restricted Delaunay Triangulation in Random Geometric Graphs
"... Abstract. Let G = G(n, r) be a random geometric graph resulting from placing n nodes uniformly at random in the unit square (disk) and connecting every two nodes if and only if their Euclidean distance is at most r. Let rcon = q log n πn be the known critical radius guaranteeing connectivity when ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
Abstract. Let G = G(n, r) be a random geometric graph resulting from placing n nodes uniformly at random in the unit square (disk) and connecting every two nodes if and only if their Euclidean distance is at most r. Let rcon = q log n πn be the known critical radius guaranteeing connectivity when n → ∞. The Restricted Delaunay Graph RDG(G) is a subgraph of G with the following properties: it is a planar graph and a spanner of G, and in particular it contains all the short edges of the Delaunay triangulation of G. While in general networks the construction of RDG(G) requires O(n) messages, we show that when r = O(rcon) and G = G(n, r), with high probability, RDG(G) can be constructed locally in one round of communication with O ( √ n log n) messages, and with only one hop neighborhood information. This proves that the existence of long Delaunay edges (an order larger than rcon) in the unit square (disk) does not significantly impact the efficiency with which good routing graphs can be maintained. 1
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 ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
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.
Raptor Codes Based Distributed Storage Algorithms for Wireless Sensor Networks
, 903
"... Abstract—We consider a distributed storage problem in a largescale wireless sensor network with n nodes among which k acquire (sense) independent data. The goal is to disseminate the acquired information throughout the network so that each of the n sensors stores one possibly coded packet and the o ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract—We consider a distributed storage problem in a largescale wireless sensor network with n nodes among which k acquire (sense) independent data. The goal is to disseminate the acquired information throughout the network so that each of the n sensors stores one possibly coded packet and the original k data packets can be recovered later in a computationally simple way from any (1 + ǫ)k of nodes for some small ǫ> 0. We propose two Raptor codes based distributed storage algorithms for solving this problem. In the first algorithm, all the sensors have the knowledge of n and k. In the second one, we assume that no sensor has such global information. I.
Frugal Routing on Wireless AdHoc Networks
"... Abstract. We study gametheoretic mechanisms for routing in adhoc networks. Gametheoretic mechanisms capture the noncooperative and selfish behavior of nodes in a resourceconstrained environment. There have been some recent proposals to use incentivebased mechanisms (in particular, VCG) for rou ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We study gametheoretic mechanisms for routing in adhoc networks. Gametheoretic mechanisms capture the noncooperative and selfish behavior of nodes in a resourceconstrained environment. There have been some recent proposals to use incentivebased mechanisms (in particular, VCG) for routing in wireless adhoc networks, and some frugality bounds are known when the connectivity graph is essentially complete. We show frugality bounds for random geometric graphs, a wellknown model for adhoc wireless connectivity. Our main result demonstrates that VCGbased routing in adhoc networks exhibits small frugality ratio (i.e., overpayment) with high probability. In addition, we study a more realistic generalization where sets of agents can form communities to maximize total profit. We also analyze the performance of VCG under such a community model and show similar bounds. While some recent truthful protocols for the traditional (individual) agent model have improved upon the frugality of VCG by selecting paths to minimize not only the cost but the overpayment, we show that extending such protocols to the community model requires solving NPcomplete problems which are provably hard to approximate. 1
Many Random Walks Are Faster Than One
, 2006
"... This paper is about searching a graph with a random walk. We show that several random walks running (or walking) in parallel can often search a graph much faster than a single random walk on its own. We measure the cover time, which is the expected amount of time required to visit every node in the ..."
Abstract
 Add to MetaCart
This paper is about searching a graph with a random walk. We show that several random walks running (or walking) in parallel can often search a graph much faster than a single random walk on its own. We measure the cover time, which is the expected amount of time required to visit every node in the graph, and we show that for a large collection of interesting graphs running many random walks in parallel yields a nearly linear speed up in the cover time. We demonstrate that an exponential speed up is sometimes possible, and that there are natural examples of graphs that allow only a logarithmic speed up.
Random walk with jumps in largescale random geometric graphs
 COMPUTER COMMUNICATIONS
, 2010
"... ..."
Clustering Based on Pairwise Distances When the Data is of Mixed Dimensions
, 909
"... Abstract. In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain theoretical guaranties for a few emblematic methods bas ..."
Abstract
 Add to MetaCart
Abstract. In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain theoretical guaranties for a few emblematic methods based on pairwise distances: a simple algorithm based on the extraction of connected components in a neighborhood graph; the spectral clustering method of Ng, Jordan and Weiss; and hierarchical clustering with single linkage. The methods are shown to enjoy some nearoptimal properties in terms of separation between clusters and robustness to outliers. The local scaling method of ZelnikManor and Perona is shown to lead to a nearoptimal choice for the scale in the first two methods. We also provide a lower bound on the spectral gap to consistently choose the correct number of clusters in the spectral method.
Science.
"... Abstract The paper considers broadcasting in radio networks, modeled as unit disk graphs (UDG). Such networks occur in wireless communication between sites (e.g., stations or sensors) situated in a terrain. Network stations are represented by points in the Euclidean plane, where a station is connect ..."
Abstract
 Add to MetaCart
Abstract The paper considers broadcasting in radio networks, modeled as unit disk graphs (UDG). Such networks occur in wireless communication between sites (e.g., stations or sensors) situated in a terrain. Network stations are represented by points in the Euclidean plane, where a station is connected to all stations at distance at most 1 from it. A message transmitted by a station reaches all its neighbors, but a station hears a message (receives the message