We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

So far, the problem of positioning in wireless networks has been studied mainly in a nonadversarial setting. In this paper, we analyze the resistance of positioning techniques to position and distance spoofing attacks. We propose a mechanism for secure positioning of wireless devices, that we call verifiable multilateration. We then show how this mechanism can be used to secure positioning in sensor networks. We analyze our system through simulations.

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Secure positioning in wireless networks

We want to express digital communication with a human touch. So we pay attention to the properties of a door because it links one place to another. We think the linking of different places and sharing of places is one of the substantial qualities of network technology. Another reason that we focus on a door is because it bears great meanings. For example, a door is the first spot for a meeting with someone or for kissing someone goodbye. It could be your children, spouse, or your friends. These days, we talk and say hello to friends by Messenger or mobiles. Accustomed to digital devices which neglect time or space, we expect that the devices can carry our emotions to others. However, these have limits in expression. We want to show through the our work "The Door" that network technology should have a little more humanity and love in the near future.

The Door

/pdf/gossiping-models-formal-analysis-of-epidemic-protocols-b9mil0ssq1.pdf

Gossiping Models : Formal Analysis of Epidemic Protocols

In this paper, we consider wireless mobile sensor networks under extreme environments where nodes: 1) have local knowledge; 2) have limited computational power; 3) make distributed decisions; and 4) move rapidly over time. Information dissemination in these networks (or gossip) can be modeled via epidemic models that analyze behavior of the system mimicking the way diseases spread (or even gossip for that matter). However, the limitation on computational power and energy of nodes forces us to consider explicit stopping criteria that are seldom done in the literature. Furthermore, harsh environments considered in this paper prevent nodes from transmitting sensed information at specified time slots and hence might cause a large variation in intertransmission time distribution. The objective of this paper is to characterize the dynamics of the information spread and obtain performance measures based on stochastic modeling. We start with modeling information flow using a Markov chain and obtain performance measures such as time to transfer information and fraction of nodes receiving information. Then, we provide a method to obtain those performance measures when the assumption on intertransmission time distribution is relaxed, e.g., time-varying transmission rates and nonexponential intertransmission time distributions, which makes our model more realistic. We make a curious finding in that, for our proposed model, the average fraction of nodes receiving information is a parameter-free constant. We also show that our model is scalable and effective.

Epidemic-based information dissemination in wireless mobile sensor networks

We investigate four performance metrics for randomized broadcast protocols on sensor networks: the fraction of nodes that receive the message (coverage), the number of first-time receivers per transmission (energy efficiency), the node-average normalized time till reception (per hop latency), and the average number of control messages per node (overhead). Our focus is to evaluate the extent to which the exchange of local information (either active or passive) can improve protocol performance. To this end we study via simulation three protocols from the literature that exploit local information (GOSSIP3 from [8], SPIN-1 from [10], and PUSH&PULL from [12])and compare their performance against the well known GOSSIP1 ([8]) protocol which does not employ any local information in making transmission decisions. Our findings are that i) local information is of course quite valuable in increasing protocol performance, and ii) it is possible to obtain high coverage and efficiency but one must then incur either increased delay or increased overhead. We study the strengths and weaknesses of the above protocols and propose the new SmartGossip protocol which combines several ideas from the above protocols, as well as several new mechanisms, to achieve superior performance.

SmartGossip: an improved randomized broadcast protocol for sensor networks

The broadcast capacity of a wireless sensor network (WSN) is defined as the maximum rate at which the network may generate messages intended for distribution to the entire network when subject to certain conditions on coverage and delay. Broadcast capacity is limited by factors such as communication collisions and congestion. Collisions may be reduced through the use of communication coordination (CC), and congestion may be reduced through information coordination (IC), ensuring that only useful messages are transmitted and stored. We study the broadcast capacity of a WSN when subject to various real world phenomena that affect wireless communication, namely channel variations, interference and random node failures. We study the benefits and costs associated with using the IC and CC mechanisms on different topologies through the use of various metrics.

Broadcast capacity of a WSN under communication and information coordination

We propose a novel framework for analyzing the dynamic performance of a gossip protocol on a graph through the use of copulas. Copulas are a statistical technique that express the joint distribution of a set of random variables as a function of their marginal distributions. Using a version of gossip appropriate for wireless networks, we model the system dynamics through equations expressed in terms of q(i, t), the probability that node i has not received by time t, and r(i, t), the probability that node i does not transmit at time t. The solution of the system equations can be used to predict the fraction of nodes that have received the message by time t, which is an important measure of gossip protocol performance. The analysis is verified with simulation results on four different network topologies: a grid, a random geometric graph, an Erd?s-Renyi graph, and a small-world graph. The model captures the system dynamics of the gossip protocol very well over a wide range of conditions.

Analysis of gossip performance with copulas

The broadcast capacity of a wireless sensor network (WSN) is defined as the maximum rate at which the network may generate messages intended for distribution to the entire network. Broadcast capacity is limited by factors such as communication collisions and excessive queue lengths incurred under heavy loads. Collisions may be avoided through the use of communication coordination (CC), and excessive queue lengths may be avoided through information coordination (IC), ensuring that only useful messages are transmitted and stored. Our communication model takes into consideration channel variations (using Rayleigh fading) and interference due to overlapping transmissions. Any node's transmission can potentially reach every other node in the network, provided that the received signal to interference plus noise ratio (SINR) at the receiver is above a certain threshold. Our results show the benefits of IC and CC as well as the tradeoffs in terms of the cost incurred when using these mechanisms.

Performance of a WSN in the Presence of Channel Variations and Interference

The broadcast capacity of a wireless sensor network (WSN) is defined as the maximum rate at which the network may generate messages intended for distribution to the entire network subject to coverage and delay constraints. Broadcast capacity depends on factors such as topology, collisions, node failures and queueing delays that may be incurred during heavy load conditions. In our previous work, we studied the improvements in efficiency and collision reduction through the use of information coordination (IC) and communication coordination (CC) respectively. In this paper we extend our work in three aspects: (i) we look at a more realistic topology for sensor networks, a Poisson cluster process, (ii) we allow for variable transmission distances as an abstraction of power control, and (iii) messages have a limited dissemination range, implying that each message may only permeate up to a certain distance r from its originator. We quantify the additional improvement in broadcast capacity when power control is added to IC and CC. We also show that broadcast capacity greatly increases when the reach of the message is restricted irrespective of whether IC and/or CC are employed, however the penalty incurred is reduced coverage.

Nikhil Singhal

Papers

SmartGossip: an improved randomized broadcast protocol for sensor networks

Broadcast capacity of a WSN under communication and information coordination

Analysis of gossip performance with copulas

Performance of a WSN in the Presence of Channel Variations and Interference

Broadcast capacity of a WSN employing power control and limited range dissemination