1,373 research outputs found
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
Online Resource Inference in Network Utility Maximization Problems
The amount of transmitted data in computer networks is expected to grow
considerably in the future, putting more and more pressure on the network
infrastructures. In order to guarantee a good service, it then becomes
fundamental to use the network resources efficiently. Network Utility
Maximization (NUM) provides a framework to optimize the rate allocation when
network resources are limited. Unfortunately, in the scenario where the amount
of available resources is not known a priori, classical NUM solving methods do
not offer a viable solution. To overcome this limitation we design an overlay
rate allocation scheme that attempts to infer the actual amount of available
network resources while coordinating the users rate allocation. Due to the
general and complex model assumed for the congestion measurements, a passive
learning of the available resources would not lead to satisfying performance.
The coordination scheme must then perform active learning in order to speed up
the resources estimation and quickly increase the system performance. By
adopting an optimal learning formulation we are able to balance the tradeoff
between an accurate estimation, and an effective resources exploitation in
order to maximize the long term quality of the service delivered to the users
Max-Weight Revisited: Sequences of Non-Convex Optimisations Solving Convex Optimisations
We investigate the connections between max-weight approaches and dual
subgradient methods for convex optimisation. We find that strong connections
exist and we establish a clean, unifying theoretical framework that includes
both max-weight and dual subgradient approaches as special cases. Our analysis
uses only elementary methods, and is not asymptotic in nature. It also allows
us to establish an explicit and direct connection between discrete queue
occupancies and Lagrange multipliers.Comment: convex optimisation, max-weight scheduling, backpressure, subgradient
method
A Decomposition Algorithm for Nested Resource Allocation Problems
We propose an exact polynomial algorithm for a resource allocation problem
with convex costs and constraints on partial sums of resource consumptions, in
the presence of either continuous or integer variables. No assumption of strict
convexity or differentiability is needed. The method solves a hierarchy of
resource allocation subproblems, whose solutions are used to convert
constraints on sums of resources into bounds for separate variables at higher
levels. The resulting time complexity for the integer problem is , and the complexity of obtaining an -approximate
solution for the continuous case is , being
the number of variables, the number of ascending constraints (such that ), a desired precision, and the total resource. This
algorithm attains the best-known complexity when , and improves it when
. Extensive experimental analyses are conducted with four
recent algorithms on various continuous problems issued from theory and
practice. The proposed method achieves a higher performance than previous
algorithms, addressing all problems with up to one million variables in less
than one minute on a modern computer.Comment: Working Paper -- MIT, 23 page
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