5,319 research outputs found
Stability of Influence Maximization
The present article serves as an erratum to our paper of the same title,
which was presented and published in the KDD 2014 conference. In that article,
we claimed falsely that the objective function defined in Section 1.4 is
non-monotone submodular. We are deeply indebted to Debmalya Mandal, Jean
Pouget-Abadie and Yaron Singer for bringing to our attention a counter-example
to that claim.
Subsequent to becoming aware of the counter-example, we have shown that the
objective function is in fact NP-hard to approximate to within a factor of
for any .
In an attempt to fix the record, the present article combines the problem
motivation, models, and experimental results sections from the original
incorrect article with the new hardness result. We would like readers to only
cite and use this version (which will remain an unpublished note) instead of
the incorrect conference version.Comment: Erratum of Paper "Stability of Influence Maximization" which was
presented and published in the KDD1
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
Outward Influence and Cascade Size Estimation in Billion-scale Networks
Estimating cascade size and nodes' influence is a fundamental task in social,
technological, and biological networks. Yet this task is extremely challenging
due to the sheer size and the structural heterogeneity of networks. We
investigate a new influence measure, termed outward influence (OI), defined as
the (expected) number of nodes that a subset of nodes will activate,
excluding the nodes in S. Thus, OI equals, the de facto standard measure,
influence spread of S minus |S|. OI is not only more informative for nodes with
small influence, but also, critical in designing new effective sampling and
statistical estimation methods.
Based on OI, we propose SIEA/SOIEA, novel methods to estimate influence
spread/outward influence at scale and with rigorous theoretical guarantees. The
proposed methods are built on two novel components 1) IICP an important
sampling method for outward influence, and 2) RSA, a robust mean estimation
method that minimize the number of samples through analyzing variance and range
of random variables. Compared to the state-of-the art for influence estimation,
SIEA is times faster in theory and up to several orders of
magnitude faster in practice. For the first time, influence of nodes in the
networks of billions of edges can be estimated with high accuracy within a few
minutes. Our comprehensive experiments on real-world networks also give
evidence against the popular practice of using a fixed number, e.g. 10K or 20K,
of samples to compute the "ground truth" for influence spread.Comment: 16 pages, SIGMETRICS 201
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