6,010 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
Sketch-based Influence Maximization and Computation: Scaling up with Guarantees
Propagation of contagion through networks is a fundamental process. It is
used to model the spread of information, influence, or a viral infection.
Diffusion patterns can be specified by a probabilistic model, such as
Independent Cascade (IC), or captured by a set of representative traces.
Basic computational problems in the study of diffusion are influence queries
(determining the potency of a specified seed set of nodes) and Influence
Maximization (identifying the most influential seed set of a given size).
Answering each influence query involves many edge traversals, and does not
scale when there are many queries on very large graphs. The gold standard for
Influence Maximization is the greedy algorithm, which iteratively adds to the
seed set a node maximizing the marginal gain in influence. Greedy has a
guaranteed approximation ratio of at least (1-1/e) and actually produces a
sequence of nodes, with each prefix having approximation guarantee with respect
to the same-size optimum. Since Greedy does not scale well beyond a few million
edges, for larger inputs one must currently use either heuristics or
alternative algorithms designed for a pre-specified small seed set size.
We develop a novel sketch-based design for influence computation. Our greedy
Sketch-based Influence Maximization (SKIM) algorithm scales to graphs with
billions of edges, with one to two orders of magnitude speedup over the best
greedy methods. It still has a guaranteed approximation ratio, and in practice
its quality nearly matches that of exact greedy. We also present influence
oracles, which use linear-time preprocessing to generate a small sketch for
each node, allowing the influence of any seed set to be quickly answered from
the sketches of its nodes.Comment: 10 pages, 5 figures. Appeared at the 23rd Conference on Information
and Knowledge Management (CIKM 2014) in Shanghai, Chin
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
Online Influence Maximization (Extended Version)
Social networks are commonly used for marketing purposes. For example, free
samples of a product can be given to a few influential social network users (or
"seed nodes"), with the hope that they will convince their friends to buy it.
One way to formalize marketers' objective is through influence maximization (or
IM), whose goal is to find the best seed nodes to activate under a fixed
budget, so that the number of people who get influenced in the end is
maximized. Recent solutions to IM rely on the influence probability that a user
influences another one. However, this probability information may be
unavailable or incomplete. In this paper, we study IM in the absence of
complete information on influence probability. We call this problem Online
Influence Maximization (OIM) since we learn influence probabilities at the same
time we run influence campaigns. To solve OIM, we propose a multiple-trial
approach, where (1) some seed nodes are selected based on existing influence
information; (2) an influence campaign is started with these seed nodes; and
(3) users' feedback is used to update influence information. We adopt the
Explore-Exploit strategy, which can select seed nodes using either the current
influence probability estimation (exploit), or the confidence bound on the
estimation (explore). Any existing IM algorithm can be used in this framework.
We also develop an incremental algorithm that can significantly reduce the
overhead of handling users' feedback information. Our experiments show that our
solution is more effective than traditional IM methods on the partial
information.Comment: 13 pages. To appear in KDD 2015. Extended versio
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