17,093 research outputs found
Exact Computation of Influence Spread by Binary Decision Diagrams
Evaluating influence spread in social networks is a fundamental procedure to
estimate the word-of-mouth effect in viral marketing. There are enormous
studies about this topic; however, under the standard stochastic cascade
models, the exact computation of influence spread is known to be #P-hard. Thus,
the existing studies have used Monte-Carlo simulation-based approximations to
avoid exact computation.
We propose the first algorithm to compute influence spread exactly under the
independent cascade model. The algorithm first constructs binary decision
diagrams (BDDs) for all possible realizations of influence spread, then
computes influence spread by dynamic programming on the constructed BDDs. To
construct the BDDs efficiently, we designed a new frontier-based search-type
procedure. The constructed BDDs can also be used to solve other
influence-spread related problems, such as random sampling without rejection,
conditional influence spread evaluation, dynamic probability update, and
gradient computation for probability optimization problems.
We conducted computational experiments to evaluate the proposed algorithm.
The algorithm successfully computed influence spread on real-world networks
with a hundred edges in a reasonable time, which is quite impossible by the
naive algorithm. We also conducted an experiment to evaluate the accuracy of
the Monte-Carlo simulation-based approximation by comparing exact influence
spread obtained by the proposed algorithm.Comment: WWW'1
Conditional Reliability in Uncertain Graphs
Network reliability is a well-studied problem that requires to measure the
probability that a target node is reachable from a source node in a
probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned
a probability of existence. Many approaches and problem variants have been
considered in the literature, all assuming that edge-existence probabilities
are fixed. Nevertheless, in real-world graphs, edge probabilities typically
depend on external conditions. In metabolic networks a protein can be converted
into another protein with some probability depending on the presence of certain
enzymes. In social influence networks the probability that a tweet of some user
will be re-tweeted by her followers depends on whether the tweet contains
specific hashtags. In transportation networks the probability that a network
segment will work properly or not might depend on external conditions such as
weather or time of the day. In this paper we overcome this limitation and focus
on conditional reliability, that is assessing reliability when edge-existence
probabilities depend on a set of conditions. In particular, we study the
problem of determining the k conditions that maximize the reliability between
two nodes. We deeply characterize our problem and show that, even employing
polynomial-time reliability-estimation methods, it is NP-hard, does not admit
any PTAS, and the underlying objective function is non-submodular. We then
devise a practical method that targets both accuracy and efficiency. We also
study natural generalizations of the problem with multiple source and target
nodes. An extensive empirical evaluation on several large, real-life graphs
demonstrates effectiveness and scalability of the proposed methods.Comment: 14 pages, 13 figure
Opinion dynamics with varying susceptibility to persuasion
A long line of work in social psychology has studied variations in people's susceptibility to persuasion -- the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people's intrinsic opinions, it is also natural to consider interventions that modify people's susceptibility to persuasion. In this work, we adopt a popular model for social opinion dynamics, and we formalize the opinion maximization and minimization problems where interventions happen at the level of susceptibility. We show that modeling interventions at the level of susceptibility lead to an interesting family of new questions in network opinion dynamics. We find that the questions are quite different depending on whether there is an overall budget constraining the number of agents we can target or not. We give a polynomial-time algorithm for finding the optimal target-set to optimize the sum of opinions when there are no budget constraints on the size of the target-set. We show that this problem is NP-hard when there is a budget, and that the objective function is neither submodular nor supermodular. Finally, we propose a heuristic for the budgeted opinion optimization and show its efficacy at finding target-sets that optimize the sum of opinions compared on real world networks, including a Twitter network with real opinion estimates
Influence Maximization Meets Efficiency and Effectiveness: A Hop-Based Approach
Influence Maximization is an extensively-studied problem that targets at
selecting a set of initial seed nodes in the Online Social Networks (OSNs) to
spread the influence as widely as possible. However, it remains an open
challenge to design fast and accurate algorithms to find solutions in
large-scale OSNs. Prior Monte-Carlo-simulation-based methods are slow and not
scalable, while other heuristic algorithms do not have any theoretical
guarantee and they have been shown to produce poor solutions for quite some
cases. In this paper, we propose hop-based algorithms that can easily scale to
millions of nodes and billions of edges. Unlike previous heuristics, our
proposed hop-based approaches can provide certain theoretical guarantees.
Experimental evaluations with real OSN datasets demonstrate the efficiency and
effectiveness of our algorithms.Comment: Extended version of the conference paper at ASONAM 2017, 11 page
Holistic Influence Maximization: Combining Scalability and Efficiency with Opinion-Aware Models
The steady growth of graph data from social networks has resulted in
wide-spread research in finding solutions to the influence maximization
problem. In this paper, we propose a holistic solution to the influence
maximization (IM) problem. (1) We introduce an opinion-cum-interaction (OI)
model that closely mirrors the real-world scenarios. Under the OI model, we
introduce a novel problem of Maximizing the Effective Opinion (MEO) of
influenced users. We prove that the MEO problem is NP-hard and cannot be
approximated within a constant ratio unless P=NP. (2) We propose a heuristic
algorithm OSIM to efficiently solve the MEO problem. To better explain the OSIM
heuristic, we first introduce EaSyIM - the opinion-oblivious version of OSIM, a
scalable algorithm capable of running within practical compute times on
commodity hardware. In addition to serving as a fundamental building block for
OSIM, EaSyIM is capable of addressing the scalability aspect - memory
consumption and running time, of the IM problem as well.
Empirically, our algorithms are capable of maintaining the deviation in the
spread always within 5% of the best known methods in the literature. In
addition, our experiments show that both OSIM and EaSyIM are effective,
efficient, scalable and significantly enhance the ability to analyze real
datasets.Comment: ACM SIGMOD Conference 2016, 18 pages, 29 figure
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