Worst-Case Scenarios for Greedy, Centrality-Based Network Protection Strategies

The task of allocating preventative resources to a computer network in order to protect against the spread of viruses is addressed. Virus spreading dynamics are described by a linearized SIS model and protection is framed by an optimization problem which maximizes the rate at which a virus in the network is contained given finite resources. One approach to problems of this type involve greedy heuristics which allocate all resources to the nodes with large centrality measures. We address the worst case performance of such greedy algorithms be constructing networks for which these greedy allocations are arbitrarily inefficient. An example application is presented in which such a worst case network might arise naturally and our results are verified numerically by leveraging recent results which allow the exact optimal solution to be computed via geometric programming

Protection against Contagion in Complex Networks

In real-world complex networks, harmful spreads, commonly known as contagions, are common and can potentially lead to catastrophic events if uncontrolled. Some examples include pandemics, network attacks on crucial infrastructure systems, and the propagation of misinformation or radical ideas. Thus, it is critical to study the protective measures that inhibit or eliminate contagion in these networks. This is known as the network protection problem. The network protection problem investigates the most efficient graph manipulations (e.g., node and/or edge removal or addition) to protect a certain set of nodes known as critical nodes. There are two types of critical nodes: (1) predefined, based on their importance to the functionality of the network; (2) unknown, whose importance depends on their location in the network structure. For both of these groups and with no assumption on the contagion dynamics, I address three major shortcomings in the current network protection research: namely, scalability, imprecise evaluation metric, and assumption on global graph knowledge. First, to address the scalability issue, I show that local community information affects contagion paths through characteristic path length. The relationship between the two suggests that, instead of global network manipulations, we can disrupt the contagion paths by manipulating the local community of critical nodes. Next, I study network protection of predefined critical nodes against targeted contagion attacks with access to partial network information only. I propose the CoVerD protection algorithm that is fast and successfully increases the attacker’s effort for reaching the target nodes by 3 to 10 times compared to the next best-performing benchmark. Finally, I study the more sophisticated problem of protecting unknown critical nodes in the context of biological contagions, with partial and no knowledge of network structure. In the presence of partial network information, I show that strategies based on immediate neighborhood information give the best trade-off between performance and cost. In the presence of no network information, I propose a dynamic algorithm, ComMit, that works within a limited budget and enforces bursts of short-term restriction on small communities instead of long-term isolation of unaffected individuals. In comparison to baselines, ComMit reduces the peak of infection by 73% and shortens the duration of infection by 90%, even for persistent spreads

Delinquent Networks

Delinquents are embedded in a network of relationships. Social ties among delinquents are modelled by means of a graph where delinquents compete for a booty and benefit from local interactions with their neighbors. Each delinquent decides in a non cooperative way how much delinquency effort he will exert. Using the network model developed by Ballester et al. (2006), we characterize the Nash equilibrium and derive an optimal enforcement policy, called the key-player policy, which targets the delinquent who, once removed, leads to the highest aggregate delinquency reduction. We then extend our characterization of optimal single player network removal for delinquency reduction, the key player, to optimal group removal, the key group. We also characterize and derive a policy that targets links rather than players. Finally, we endogenize the network connecting delinquents by allowing players to join the labor market instead of committing delinquent offenses. The key-player policy turns out to be much more complex since it depends on wages and on the structure of the network.Social networks, delinquency decision, key group, NP-hard problem, crime policies

Optimal Resource Allocation for Network Protection Against Spreading Processes

We study the problem of containing spreading processes in arbitrary directed networks by distributing protection resources throughout the nodes of the network. We consider two types of protection resources are available: (i) Preventive resources able to defend nodes against the spreading (such as vaccines in a viral infection process), and (ii) corrective resources able to neutralize the spreading after it has reached a node (such as antidotes). We assume that both preventive and corrective resources have an associated cost and study the problem of finding the cost-optimal distribution of resources throughout the nodes of the network. We analyze these questions in the context of viral spreading processes in directed networks. We study the following two problems: (i) Given a fixed budget, find the optimal allocation of preventive and corrective resources in the network to achieve the highest level of containment, and (ii) when a budget is not specified, find the minimum budget required to control the spreading process. We show that both resource allocation problems can be solved in polynomial time using Geometric Programming (GP) for arbitrary directed graphs of nonidentical nodes and a wide class of cost functions. Furthermore, our approach allows to optimize simultaneously over both preventive and corrective resources, even in the case of cost functions being node-dependent. We illustrate our approach by designing optimal protection strategies to contain an epidemic outbreak that propagates through an air transportation network

Determining the Most Vital Arcs within a Multi-Mode Communication Network Using Set-Based Measures

Technology has dramatically changed the way the military has disseminated information over the last fifty years. The Air Force has adapted to the change by operating a network with various ways to disseminate information. The Air Operating Center (AOC) is a large contributor to disseminating information in the Air Force. When the standard mode of sending information is disrupted, the AOC seeks both alternative ways available to send information and long term approaches to decrease vulnerability of its standard procedures. In this thesis, we seek to identify and quantify the most vital components within a multi-mode communications network via a combination of a set-based efficiency and set-based cost efficiency measures that utilize the all pairs shortest path (APSP) problem and minimum cost flow (MCF) problem. We capture the phenomenon that network components must work together to provide flow by examining how the network performs when sets of arcs are disrupted. We run 125 different computational experiments examining varying degrees of damage experienced by the network. From these results, we deduce insights into the characteristics of the most vital arcs in a multi-mode communication network which can inform future fortification decisions