5,698 research outputs found
Epidemic Spreading with External Agents
We study epidemic spreading processes in large networks, when the spread is
assisted by a small number of external agents: infection sources with bounded
spreading power, but whose movement is unrestricted vis-\`a-vis the underlying
network topology. For networks which are `spatially constrained', we show that
the spread of infection can be significantly speeded up even by a few such
external agents infecting randomly. Moreover, for general networks, we derive
upper-bounds on the order of the spreading time achieved by certain simple
(random/greedy) external-spreading policies. Conversely, for certain common
classes of networks such as line graphs, grids and random geometric graphs, we
also derive lower bounds on the order of the spreading time over all
(potentially network-state aware and adversarial) external-spreading policies;
these adversarial lower bounds match (up to logarithmic factors) the spreading
time achieved by an external agent with a random spreading policy. This
demonstrates that random, state-oblivious infection-spreading by an external
agent is in fact order-wise optimal for spreading in such spatially constrained
networks
Distributed convergence to Nash equilibria in two-network zero-sum games
This paper considers a class of strategic scenarios in which two networks of
agents have opposing objectives with regards to the optimization of a common
objective function. In the resulting zero-sum game, individual agents
collaborate with neighbors in their respective network and have only partial
knowledge of the state of the agents in the other network. For the case when
the interaction topology of each network is undirected, we synthesize a
distributed saddle-point strategy and establish its convergence to the Nash
equilibrium for the class of strictly concave-convex and locally Lipschitz
objective functions. We also show that this dynamics does not converge in
general if the topologies are directed. This justifies the introduction, in the
directed case, of a generalization of this distributed dynamics which we show
converges to the Nash equilibrium for the class of strictly concave-convex
differentiable functions with locally Lipschitz gradients. The technical
approach combines tools from algebraic graph theory, nonsmooth analysis,
set-valued dynamical systems, and game theory
Maximizing Algebraic Connectivity of Constrained Graphs in Adversarial Environments
This paper aims to maximize algebraic connectivity of networks via topology
design under the presence of constraints and an adversary. We are concerned
with three problems. First, we formulate the concave maximization topology
design problem of adding edges to an initial graph, which introduces a
nonconvex binary decision variable, in addition to subjugation to general
convex constraints on the feasible edge set. Unlike previous methods, our
method is justifiably not greedy and capable of accommodating these additional
constraints. We also study a scenario in which a coordinator must selectively
protect edges of the network from a chance of failure due to a physical
disturbance or adversarial attack. The coordinator needs to strategically
respond to the adversary's action without presupposed knowledge of the
adversary's feasible attack actions. We propose three heuristic algorithms for
the coordinator to accomplish the objective and identify worst-case preventive
solutions. Each algorithm is shown to be effective in simulation and we provide
some discussion on their compared performance.Comment: 8 pages, submitted to European Control Conference 201
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