In this paper, we address the problem of broadcasting in a wireless network under a novel communication model: the swamping communication model. In this model, nodes communicate only with those nodes at geometric distance greater than @math and at most @math from them. Communication between nearby nodes under this model can be very time consuming, as the length of the path between two nodes within distance @math is only bounded above by the diameter @math , in many cases. For the @math -node lattice networks, we present algorithms of optimal time complexity, respectively @math for the lattice line and @math for the two-dimensional lattice. We also consider networks of unknown topology of diameter @math and of a parameter @math ( granularity ). More specifically, we consider networks with @math the minimum distance between any two nodes and @math . We present broadcast algorithms for networks of nodes placed on the line and on the plane with respective time complexities @math and @math , where @math .
The fundamental questions of network reliability have received much attention in the context of wired networks, under the assumption that components fail randomly and independently (cf., e.g. @cite_14 @cite_23 @cite_18 @cite_12 and the survey @cite_6 ). On the other hand, empirical work has shown that positive correlation of faults is a more reasonable assumption for networks @cite_22 @cite_3 @cite_11 . In particular, in @cite_11 , the authors provide empirical evidence that data packets losses are spatially correlated in networks. Moreover, in @cite_22 , the authors state that the environment provides many phenomena that may lead to spatially correlated faults. More recently, in @cite_1 , a gap was demonstrated between the fault-tolerance of networks when faults occur independently as opposed to when they occur with positive correlation. To the best of our knowledge, this was the first paper to provide analytic results concerning network fault-tolerant communication in the presence of positively correlated faults for arbitrary networks.
@cite_18 @cite_14 @cite_22 @cite_1 @cite_6 @cite_3 @cite_23 @cite_12 @cite_11
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The aim of this paper is to study communication in networks where nodes fail in a random dependent way. In order to capture fault dependencies, we introduce the neighborhood fault model, where damaging events, called spots, occur randomly and independently with probability p at nodes of a network, and cause faults in the given node and all of its neighbors. Faults at distance at most 2 become dependent in this model and are positively correlated. We investigate the impact of spot probability on feasibility and time of communication in the fault-free part of the network. We show a network which supports fast communication with high probability, if p = 1 c log n. We also show that communication is not feasible with high probability in most classes of networks, for constant spot probabilities. For smaller spot probabilities, high probability communication is supported even by bounded degree networks. It is shown that the torus supports communication with high probability when p decreases faster than 1 n1 2, and does not when p ? 1 O(n1 2). Furthermore, a network built of tori is designed, with the same faulttolerance properties and additionally supporting fast communication. We show, however, that networks of degree bounded by a constant d do not support communication with high probability, if p ? 1 O(n1 d). While communication in networks with independent faults was widely studied, this is the first analytic paper which investigates network communication for random dependent faults. We consider the problem of identifying the source of failure in a network after receiving alarms or having observed symptoms. To locate the root cause accurately and timely in a large communication system is challenging because a single fault can often result in a large number of alarms, and multiple faults can occur concurrently. In this paper, we present a new fault localization method using a machine-learning approach. We propose to use logistic regression to study the correlation among network events based on end-to-end measurements. Then based on the regression model, we develop fault hypothesis that best explains the observed symptoms. Unlike previous work, the machine-learning algorithm requires neither the knowledge of dependencies among network events, nor the probabilities of faults, nor the conditional probabilities of fault propagation as input. The “low requirement” feature makes it suitable for large complex networks where accurate dependencies and prior probabilities are difficult to obtain. We then evaluate the performance of the learning algorithm with respect to the accuracy of fault hypothesis and the concentration property. Experimental results and theoretical analysis both show satisfactory performance. Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network1. Complex communication networks2 display a surprising degree of robustness: although key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these and other complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneously wired networks, called scale-free networks, which include the World-Wide Web3,4,5, the Internet6, social networks7 and cells8. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network's connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks. In this paper we consider the problem of maximizing the number of supported connections in arbitrary wireless networks where a transmission is supported if and only if the signal-to-interference-plus-noise ratio at the receiver is greater than some threshold. The aim is to choose transmission powers for each connection so as to maximize the number of connections for which this threshold is met. We believe that analyzing this problem is important both in its own right and also because it arises as a subproblem in many other areas of wireless networking. We study both the complexity of the problem and also present some game theoretic results regarding capacity that is achieved by completely distributed algorithms. We also feel that this problem is intriguing since it involves both continuous aspects (i.e. choosing the transmission powers) as well as discrete aspects (i.e. which connections should be supported). Our results are: ldr We show that maximizing the number of supported connections is NP-hard, even when there is no background noise. This is in contrast to the problem of determining whether or not a given set of connections is feasible since that problem can be solved via linear programming. ldr We present a number of approximation algorithms for the problem. All of these approximation algorithms run in polynomial time and have an approximation ratio that is independent of the number of connections. ldr We examine a completely distributed algorithm and analyze it as a game in which a connection receives a positive payoff if it is successful and a negative payoff if it is unsuccessful while transmitting with nonzero power. We show that in this game there is not necessarily a pure Nash equilibrium but if such an equilibrium does exist the corresponding price of anarchy is independent of the number of connections. We also show that a mixed Nash equilibrium corresponds to a probabilistic transmission strategy and in this case such an equilibrium always exists and has a price of anarchy that is independent of the number of connections. This work was supported by NSF contract CCF-0728980 and was performed while the second author was visiting Bell Labs in Summer, 2008.