29,392 research outputs found
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
Trading Safety Versus Performance: Rapid Deployment of Robotic Swarms with Robust Performance Constraints
In this paper we consider a stochastic deployment problem, where a robotic
swarm is tasked with the objective of positioning at least one robot at each of
a set of pre-assigned targets while meeting a temporal deadline. Travel times
and failure rates are stochastic but related, inasmuch as failure rates
increase with speed. To maximize chances of success while meeting the deadline,
a control strategy has therefore to balance safety and performance. Our
approach is to cast the problem within the theory of constrained Markov
Decision Processes, whereby we seek to compute policies that maximize the
probability of successful deployment while ensuring that the expected duration
of the task is bounded by a given deadline. To account for uncertainties in the
problem parameters, we consider a robust formulation and we propose efficient
solution algorithms, which are of independent interest. Numerical experiments
confirming our theoretical results are presented and discussed
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