1,402 research outputs found
Infection Spreading and Source Identification: A Hide and Seek Game
The goal of an infection source node (e.g., a rumor or computer virus source)
in a network is to spread its infection to as many nodes as possible, while
remaining hidden from the network administrator. On the other hand, the network
administrator aims to identify the source node based on knowledge of which
nodes have been infected. We model the infection spreading and source
identification problem as a strategic game, where the infection source and the
network administrator are the two players. As the Jordan center estimator is a
minimax source estimator that has been shown to be robust in recent works, we
assume that the network administrator utilizes a source estimation strategy
that can probe any nodes within a given radius of the Jordan center. Given any
estimation strategy, we design a best-response infection strategy for the
source. Given any infection strategy, we design a best-response estimation
strategy for the network administrator. We derive conditions under which a Nash
equilibrium of the strategic game exists. Simulations in both synthetic and
real-world networks demonstrate that our proposed infection strategy infects
more nodes while maintaining the same safety margin between the true source
node and the Jordan center source estimator
Identifying Infection Sources and Regions in Large Networks
Identifying the infection sources in a network, including the index cases
that introduce a contagious disease into a population network, the servers that
inject a computer virus into a computer network, or the individuals who started
a rumor in a social network, plays a critical role in limiting the damage
caused by the infection through timely quarantine of the sources. We consider
the problem of estimating the infection sources and the infection regions
(subsets of nodes infected by each source) in a network, based only on
knowledge of which nodes are infected and their connections, and when the
number of sources is unknown a priori. We derive estimators for the infection
sources and their infection regions based on approximations of the infection
sequences count. We prove that if there are at most two infection sources in a
geometric tree, our estimator identifies the true source or sources with
probability going to one as the number of infected nodes increases. When there
are more than two infection sources, and when the maximum possible number of
infection sources is known, we propose an algorithm with quadratic complexity
to estimate the actual number and identities of the infection sources.
Simulations on various kinds of networks, including tree networks, small-world
networks and real world power grid networks, and tests on two real data sets
are provided to verify the performance of our estimators
Finding Rumor Sources on Random Trees
We consider the problem of detecting the source of a rumor which has spread
in a network using only observations about which set of nodes are infected with
the rumor and with no information as to \emph{when} these nodes became
infected. In a recent work \citep{ref:rc} this rumor source detection problem
was introduced and studied. The authors proposed the graph score function {\em
rumor centrality} as an estimator for detecting the source. They establish it
to be the maximum likelihood estimator with respect to the popular Susceptible
Infected (SI) model with exponential spreading times for regular trees. They
showed that as the size of the infected graph increases, for a path graph
(2-regular tree), the probability of source detection goes to while for
-regular trees with the probability of detection, say ,
remains bounded away from and is less than . However, their results
stop short of providing insights for the performance of the rumor centrality
estimator in more general settings such as irregular trees or the SI model with
non-exponential spreading times.
This paper overcomes this limitation and establishes the effectiveness of
rumor centrality for source detection for generic random trees and the SI model
with a generic spreading time distribution. The key result is an interesting
connection between a continuous time branching process and the effectiveness of
rumor centrality. Through this, it is possible to quantify the detection
probability precisely. As a consequence, we recover all previous results as a
special case and obtain a variety of novel results including the {\em
universality} of rumor centrality in the context of tree-like graphs and the SI
model with a generic spreading time distribution.Comment: 38 pages, 6 figure
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