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Information Source Detection with Limited Time Knowledge
This paper investigates the problem of utilizing network topology and partial
timestamps to detect the information source in a network. The problem incurs
prohibitive cost under canonical maximum likelihood estimation (MLE) of the
source due to the exponential number of possible infection paths. Our main idea
of source detection, however, is to approximate the MLE by an alternative
infection path based estimator, the essence of which is to identify the most
likely infection path that is consistent with observed timestamps. The source
node associated with that infection path is viewed as the estimated source
. We first study the case of tree topology, where by transforming the
infection path based estimator into a linear integer programming, we find a
reduced search region that remarkably improves the time efficiency. Within this
reduced search region, the estimator is provably always on a path
which we term as \emph{candidate path}. This notion enables us to analyze the
distribution of , the error distance between and
the true source , on arbitrary tree, which allows us to obtain for
the first time, in the literature provable performance guarantee of the
estimator under limited timestamps. Specifically, on the infinite -regular
tree with uniform sampled timestamps, we get a refined performance guarantee in
the sense of a constant bounded . By virtue of time
labeled BFS tree, the estimator still performs fairly well when extended to
more general graphs. Experiments on both synthetic and real datasets further
demonstrate the superior performance of our proposed algorithms.Comment: 15 page