Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

Essays in network theory applications for transportation planning

Abstract: Throughout the dissertation, network methods are developed to address pressing issues in transportation science and geography. These methods are applied to case studies to highlight their use for urban planners and social scientists working in transportation, mobility, housing, and health. The first chapter introduces novel network robustness measures for multi-line networks. This work will provide transportation planners a new tool for evaluating the resilience of transportation systems with multiple lines to failures. The second chapter explores optimizing network connectivity to maximize the number of nodes within a given distance to a focal node while minimizing the number and length of additional connections. These methods can be used to identify optimal thoroughfare design around important facilities, such as schools. The third chapter utilizes the network optimization heuristics presented in Chapter 2 to identify the impact of thoroughfare connectivity on student active commuting. Housing developers can incorporate these findings when planning new residential developments around schools. The dissertation concludes with future directions in this research domain.

Inverse problems in networks

Abstract: The recent impressive growth of Internet in the last two decades lead to an increased need of techniques to measure its structure and its performance. Network measurement methods can broadly be classified into passive methods that rely on data collected at routers, and active methods based on observations of actively-injected probe packets. Active measurement, which are the motivation of this dissertation, are attractive to end-users who, under the current Internet architecture, cannot access any measurement data collected at routers. On another side, network theory has been developed for over one century, and many tools are available to predict the performance of a system, depending on a few key parameters. Queueing theory emerges as one particularly fruitful network theory both for telephone services and wired packet-switching networks. In the latter case, queuing theory focuses on the packet-level mechanisms and predicts packet-level statistics. At the flow-level viewpoint, the theory of bandwidth sharing networks is a powerful abstraction of any bandwidth allocation scheme, including the implicit bandwidth sharing performed by the Transfer Control Protocol. There has been many works showing how the results stemming from these theories can be applied to real networks, in particular to the Internet, and in which aspects real network behaviour differs from the theoretical prediction. However, there has been up to now very few works linking this theoretical viewpoint of networks and the practical problem of network measurement. In this dissertation, we aim at building a few bridges between the world of network active probing techniques and the world of network theory. We adopt the approach of inverse problems. Inverse problems are best seen in opposition to direct problems. A direct problem predicts the evolution of some specified systems, depending on the initial conditions and some known evolution equation. An inverse problem observes part of the trajectory of the system, and aims at estimating the initial condition or parameters that can lead to such an evolution . Active probing technique inputs are the delay and loss time series of the probes, which are precisely a part of the trajectory of the network. Hence, active probing techniques can be seen as inverse problems for some network theory which could predict correctly the evolution of networks. In this dissertation, we show how active probing techniques are linked to inverse problems in queueing theory. We specify how the active probing constraint can be added to the inverse problems, what are the observables, and detail the different steps for an inverse problem in queueing theory. We classify these problems in three different categories, depending on their output and their generality, and give some simple examples to illustrate their different properties. We then investigate in detail one specific inverse problem, where the network behaves as a Kelly network with K servers in tandem. In this specific case, we are able to compute the explicit distribution of the probe end-to-end delays, depending on the residual capacities on each server and the probing intensity. We show that the set of residual capacities can be inferred from the mean end-to-end probe delay for K different probe intensities. We provide an alternative inversion technique, based on the distribution of the probe delays for a single probing intensity. In the case of two servers, we give an explicit characterization of the maximum likelihood estimator of the residual capacities. In the general case, we use the Expectation-Maximization algorithm (E-M). We prove that in the case of two servers, the estimation of E-M converges to a finite limit, which is a solution of the likelihood equation. We provide an explicit formula for the computation of the iteration step when K = 2 or K = 3, and show that the formula stays tractable for any number of servers. We evaluate these techniques numerically. Based on simulations fed with real network traces, we study independently the impact of the assumptions of a Kelly network on the performance of the estimator, and provide simple correction factors when they are needed. We also extend the previous example to the case of a tree-shaped network. The probes are multicast, originated from the root and destined to the leaves. They experience an exponentially distributed waiting time at each node. We show how this model is related to the model of a tree-shaped Kelly network with unicast cross-traffic and multicast probes, and provide an explicit formula for the likelihood of the joint delays. We use the E-M algorithm to compute the maximum likelihood estimators of the mean delay in each node, and derive explicit solutions for the combined E andMsteps. Numerical simulations illustrate the convergence properties of the estimator. As E-M is slow in this case, we provide a technique for convergence acceleration of the algorithm, allowing much larger trees to be considered as would otherwise be the case. This technique has some novel features and may be of broader interest. Finally, we explore the case of inverse problems in the theory of bandwidth sharing networks. Using two simple examples of networks, we show how a prober can measure the network by varying the number of probing flows and measure the associated bandwidth allocated to each probing flow. In particular, when the bandwidth allocation maximizes an -fair utility function, the set of server capacities and their associated flow numbers can be uniquely identified in most cases. We provide an explicit algorithm for this inversion, with some cases illustrating the numerical properties of the technique.

Controlling the katz-bonacich centrality in social network: application to gossip in online social networks

Abstract: Recent papers studied the control of spectral centrality measures of a network by manipulating the topology of the network. We extend these works by focusing on a specific spectral centrality measure, the Katz-Bonacich centrality. The optimization of the Katz-Bonacich centrality using a topological control is called the Katz-Bonacich optimization problem. We first prove that this problem is equivalent to a linear optimization problem. Thus, in the context of large graphs, we can use state of the art algorithms. We provide a specific applications of the Katz-Bonacich centrality minimization problem based on the minimization of gossip propagation and make some experiments on real networks.

Temporal Centrality Prediction in Opportunistic Mobile Social Networks

Abstract: In this paper, we focus on predicting nodes' future importance under three important metrics, namely betweenness, and closeness centrality, using real mobility traces in Opportunistic Mobile Social Networks OMSNs. Through real trace-driven simulations, we find that nodes' importance is highly predictable due to natural social behaviour of human. Then, based on the observations in the simulation, we design several reasonable prediction methods to predict nodes' future temporal centrality. Finally, extensive real trace-driven simulations are conducted to evaluate the performance of our proposed methods. The results show that the Recent Uniform Average method performs best when predicting the future Betweenness centrality, and the Periodical Average Method performs best when predicting the future Closeness centrality in the MIT Reality trace. Moreover, the Recent Uniform Average method performs best in the Infocom 06 trace.