6 research outputs found
Minimizing Seed Set Selection with Probabilistic Coverage Guarantee in a Social Network
A topic propagating in a social network reaches its tipping point if the
number of users discussing it in the network exceeds a critical threshold such
that a wide cascade on the topic is likely to occur. In this paper, we consider
the task of selecting initial seed users of a topic with minimum size so that
with a guaranteed probability the number of users discussing the topic would
reach a given threshold. We formulate the task as an optimization problem
called seed minimization with probabilistic coverage guarantee (SM-PCG). This
problem departs from the previous studies on social influence maximization or
seed minimization because it considers influence coverage with probabilistic
guarantees instead of guarantees on expected influence coverage. We show that
the problem is not submodular, and thus is harder than previously studied
problems based on submodular function optimization. We provide an approximation
algorithm and show that it approximates the optimal solution with both a
multiplicative ratio and an additive error. The multiplicative ratio is tight
while the additive error would be small if influence coverage distributions of
certain seed sets are well concentrated. For one-way bipartite graphs we
analytically prove the concentration condition and obtain an approximation
algorithm with an multiplicative ratio and an
additive error, where is the total number of nodes in the social graph.
Moreover, we empirically verify the concentration condition in real-world
networks and experimentally demonstrate the effectiveness of our proposed
algorithm comparing to commonly adopted benchmark algorithms.Comment: Conference version will appear in KDD 201
Efficient Approximation Algorithms for Adaptive Seed Minimization
As a dual problem of influence maximization, the seed minimization problem
asks for the minimum number of seed nodes to influence a required number
of users in a given social network . Existing algorithms for seed
minimization mostly consider the non-adaptive setting, where all seed nodes are
selected in one batch without observing how they may influence other users. In
this paper, we study seed minimization in the adaptive setting, where the seed
nodes are selected in several batches, such that the choice of a batch may
exploit information about the actual influence of the previous batches. We
propose a novel algorithm, ASTI, which addresses the adaptive seed minimization
problem in expected
time and offers an approximation guarantee of in expectation, where is the
targeted number of influenced nodes, is size of each seed node batch, and
is a user-specified parameter. To the best of our
knowledge, ASTI is the first algorithm that provides such an approximation
guarantee without incurring prohibitive computation overhead. With extensive
experiments on a variety of datasets, we demonstrate the effectiveness and
efficiency of ASTI over competing methods.Comment: A short version of the paper appeared in 2019 International
Conference on Management of Data (SIGMOD '19), June 30--July 5, 2019,
Amsterdam, Netherlands. ACM, New York, NY, USA, 18 page