28,162 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cite and use this version (which will remain an unpublished note) instead of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
Maximizing the Diversity of Exposure in a Social Network
Social-media platforms have created new ways for citizens to stay informed
and participate in public debates. However, to enable a healthy environment for
information sharing, social deliberation, and opinion formation, citizens need
to be exposed to sufficiently diverse viewpoints that challenge their
assumptions, instead of being trapped inside filter bubbles. In this paper, we
take a step in this direction and propose a novel approach to maximize the
diversity of exposure in a social network. We formulate the problem in the
context of information propagation, as a task of recommending a small number of
news articles to selected users. We propose a realistic setting where we take
into account content and user leanings, and the probability of further sharing
an article. This setting allows us to capture the balance between maximizing
the spread of information and ensuring the exposure of users to diverse
viewpoints.
The resulting problem can be cast as maximizing a monotone and submodular
function subject to a matroid constraint on the allocation of articles to
users. It is a challenging generalization of the influence maximization
problem. Yet, we are able to devise scalable approximation algorithms by
introducing a novel extension to the notion of random reverse-reachable sets.
We experimentally demonstrate the efficiency and scalability of our algorithm
on several real-world datasets
Fast Detection of Community Structures using Graph Traversal in Social Networks
Finding community structures in social networks is considered to be a
challenging task as many of the proposed algorithms are computationally
expensive and does not scale well for large graphs. Most of the community
detection algorithms proposed till date are unsuitable for applications that
would require detection of communities in real-time, especially for massive
networks. The Louvain method, which uses modularity maximization to detect
clusters, is usually considered to be one of the fastest community detection
algorithms even without any provable bound on its running time. We propose a
novel graph traversal-based community detection framework, which not only runs
faster than the Louvain method but also generates clusters of better quality
for most of the benchmark datasets. We show that our algorithms run in O(|V | +
|E|) time to create an initial cover before using modularity maximization to
get the final cover.
Keywords - community detection; Influenced Neighbor Score; brokers; community
nodes; communitiesComment: 29 pages, 9 tables, and 13 figures. Accepted in "Knowledge and
Information Systems", 201
How to Influence People with Partial Incentives
We study the power of fractional allocations of resources to maximize
influence in a network. This work extends in a natural way the well-studied
model by Kempe, Kleinberg, and Tardos (2003), where a designer selects a
(small) seed set of nodes in a social network to influence directly, this
influence cascades when other nodes reach certain thresholds of neighbor
influence, and the goal is to maximize the final number of influenced nodes.
Despite extensive study from both practical and theoretical viewpoints, this
model limits the designer to a binary choice for each node, with no way to
apply intermediate levels of influence. This model captures some settings
precisely, e.g. exposure to an idea or pathogen, but it fails to capture very
relevant concerns in others, for example, a manufacturer promoting a new
product by distributing five "20% off" coupons instead of giving away one free
product.
While fractional versions of problems tend to be easier to solve than
integral versions, for influence maximization, we show that the two versions
have essentially the same computational complexity. On the other hand, the two
versions can have vastly different solutions: the added flexibility of
fractional allocation can lead to significantly improved influence. Our main
theoretical contribution is to show how to adapt the major positive results
from the integral case to the fractional case. Specifically, Mossel and Roch
(2006) used the submodularity of influence to obtain their integral results; we
introduce a new notion of continuous submodularity, and use this to obtain
matching fractional results. We conclude that we can achieve the same greedy
-approximation for the fractional case as the integral case.
In practice, we find that the fractional model performs substantially better
than the integral model, according to simulations on real-world social network
data
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