2,016 research outputs found
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
Benchmarking Measures of Network Influence
Identifying key agents for the transmission of diseases (ideas, technology,
etc.) across social networks has predominantly relied on measures of centrality
on a static base network or a temporally flattened graph of agent interactions.
Various measures have been proposed as the best trackers of influence, such as
degree centrality, betweenness, and -shell, depending on the structure of
the connectivity. We consider SIR and SIS propagation dynamics on a
temporally-extruded network of observed interactions and measure the
conditional marginal spread as the change in the magnitude of the infection
given the removal of each agent at each time: its temporal knockout (TKO)
score. We argue that the exhaustive approach of the TKO score makes it an
effective benchmark measure for evaluating the accuracy of other, often more
practical, measures of influence. We find that none of the common network
measures applied to the induced flat graphs are accurate predictors of network
propagation influence on the systems studied; however, temporal networks and
the TKO measure provide the requisite targets for the hunt for effective
predictive measures
Optimal Vaccine Allocation to Control Epidemic Outbreaks in Arbitrary Networks
We consider the problem of controlling the propagation of an epidemic
outbreak in an arbitrary contact network by distributing vaccination resources
throughout the network. We analyze a networked version of the
Susceptible-Infected-Susceptible (SIS) epidemic model when individuals in the
network present different levels of susceptibility to the epidemic. In this
context, controlling the spread of an epidemic outbreak can be written as a
spectral condition involving the eigenvalues of a matrix that depends on the
network structure and the parameters of the model. We study the problem of
finding the optimal distribution of vaccines throughout the network to control
the spread of an epidemic outbreak. We propose a convex framework to find
cost-optimal distribution of vaccination resources when different levels of
vaccination are allowed. We also propose a greedy approach with quality
guarantees for the case of all-or-nothing vaccination. We illustrate our
approaches with numerical simulations in a real social network
Containing epidemic outbreaks by message-passing techniques
The problem of targeted network immunization can be defined as the one of
finding a subset of nodes in a network to immunize or vaccinate in order to
minimize a tradeoff between the cost of vaccination and the final (stationary)
expected infection under a given epidemic model. Although computing the
expected infection is a hard computational problem, simple and efficient
mean-field approximations have been put forward in the literature in recent
years. The optimization problem can be recast into a constrained one in which
the constraints enforce local mean-field equations describing the average
stationary state of the epidemic process. For a wide class of epidemic models,
including the susceptible-infected-removed and the
susceptible-infected-susceptible models, we define a message-passing approach
to network immunization that allows us to study the statistical properties of
epidemic outbreaks in the presence of immunized nodes as well as to find
(nearly) optimal immunization sets for a given choice of parameters and costs.
The algorithm scales linearly with the size of the graph and it can be made
efficient even on large networks. We compare its performance with topologically
based heuristics, greedy methods, and simulated annealing
Traffic Control for Network Protection Against Spreading Processes
Epidemic outbreaks in human populations are facilitated by the underlying
transportation network. We consider strategies for containing a viral spreading
process by optimally allocating a limited budget to three types of protection
resources: (i) Traffic control resources, (ii), preventative resources and
(iii) corrective resources. Traffic control resources are employed to impose
restrictions on the traffic flowing across directed edges in the transportation
network. Preventative resources are allocated to nodes to reduce the
probability of infection at that node (e.g. vaccines), and corrective resources
are allocated to nodes to increase the recovery rate at that node (e.g.
antidotes). We assume these resources have monetary costs associated with them,
from which we formalize an optimal budget allocation problem which maximizes
containment of the infection. We present a polynomial time solution to the
optimal budget allocation problem using Geometric Programming (GP) for an
arbitrary weighted and directed contact network and a large class of resource
cost functions. We illustrate our approach by designing optimal traffic control
strategies to contain an epidemic outbreak that propagates through a real-world
air transportation network.Comment: arXiv admin note: text overlap with arXiv:1309.627
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
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