4,639 research outputs found
Adaptive Greedy versus Non-adaptive Greedy for Influence Maximization
We consider the \emph{adaptive influence maximization problem}: given a
network and a budget , iteratively select seeds in the network to
maximize the expected number of adopters. In the \emph{full-adoption feedback
model}, after selecting each seed, the seed-picker observes all the resulting
adoptions. In the \emph{myopic feedback model}, the seed-picker only observes
whether each neighbor of the chosen seed adopts. Motivated by the extreme
success of greedy-based algorithms/heuristics for influence maximization, we
propose the concept of \emph{greedy adaptivity gap}, which compares the
performance of the adaptive greedy algorithm to its non-adaptive counterpart.
Our first result shows that, for submodular influence maximization, the
adaptive greedy algorithm can perform up to a -fraction worse than the
non-adaptive greedy algorithm, and that this ratio is tight. More specifically,
on one side we provide examples where the performance of the adaptive greedy
algorithm is only a fraction of the performance of the non-adaptive
greedy algorithm in four settings: for both feedback models and both the
\emph{independent cascade model} and the \emph{linear threshold model}. On the
other side, we prove that in any submodular cascade, the adaptive greedy
algorithm always outputs a -approximation to the expected number of
adoptions in the optimal non-adaptive seed choice. Our second result shows
that, for the general submodular cascade model with full-adoption feedback, the
adaptive greedy algorithm can outperform the non-adaptive greedy algorithm by
an unbounded factor. Finally, we propose a risk-free variant of the adaptive
greedy algorithm that always performs no worse than the non-adaptive greedy
algorithm.Comment: 26 pages, 0 figure, accepted at AAAI'20: Thirty-Fourth AAAI
Conference on Artificial Intelligenc
Combining Traditional Marketing and Viral Marketing with Amphibious Influence Maximization
In this paper, we propose the amphibious influence maximization (AIM) model
that combines traditional marketing via content providers and viral marketing
to consumers in social networks in a single framework. In AIM, a set of content
providers and consumers form a bipartite network while consumers also form
their social network, and influence propagates from the content providers to
consumers and among consumers in the social network following the independent
cascade model. An advertiser needs to select a subset of seed content providers
and a subset of seed consumers, such that the influence from the seed providers
passing through the seed consumers could reach a large number of consumers in
the social network in expectation.
We prove that the AIM problem is NP-hard to approximate to within any
constant factor via a reduction from Feige's k-prover proof system for 3-SAT5.
We also give evidence that even when the social network graph is trivial (i.e.
has no edges), a polynomial time constant factor approximation for AIM is
unlikely. However, when we assume that the weighted bi-adjacency matrix that
describes the influence of content providers on consumers is of constant rank,
a common assumption often used in recommender systems, we provide a
polynomial-time algorithm that achieves approximation ratio of
for any (polynomially small) . Our
algorithmic results still hold for a more general model where cascades in
social network follow a general monotone and submodular function.Comment: An extended abstract appeared in the Proceedings of the 16th ACM
Conference on Economics and Computation (EC), 201
Probing Limits of Information Spread with Sequential Seeding
We consider here information spread which propagates with certain probability
from nodes just activated to their not yet activated neighbors. Diffusion
cascades can be triggered by activation of even a small set of nodes. Such
activation is commonly performed in a single stage. A novel approach based on
sequential seeding is analyzed here resulting in three fundamental
contributions. First, we propose a coordinated execution of randomized choices
to enable precise comparison of different algorithms in general. We apply it
here when the newly activated nodes at each stage of spreading attempt to
activate their neighbors. Then, we present a formal proof that sequential
seeding delivers at least as large coverage as the single stage seeding does.
Moreover, we also show that, under modest assumptions, sequential seeding
achieves coverage provably better than the single stage based approach using
the same number of seeds and node ranking. Finally, we present experimental
results showing how single stage and sequential approaches on directed and
undirected graphs compare to the well-known greedy approach to provide the
objective measure of the sequential seeding benefits. Surprisingly, applying
sequential seeding to a simple degree-based selection leads to higher coverage
than achieved by the computationally expensive greedy approach currently
considered to be the best heuristic
Fast and simple decycling and dismantling of networks
Decycling and dismantling of complex networks are underlying many important
applications in network science. Recently these two closely related problems
were tackled by several heuristic algorithms, simple and considerably
sub-optimal, on the one hand, and time-consuming message-passing ones that
evaluate single-node marginal probabilities, on the other hand. In this paper
we propose a simple and extremely fast algorithm, CoreHD, which recursively
removes nodes of the highest degree from the -core of the network. CoreHD
performs much better than all existing simple algorithms. When applied on
real-world networks, it achieves equally good solutions as those obtained by
the state-of-art iterative message-passing algorithms at greatly reduced
computational cost, suggesting that CoreHD should be the algorithm of choice
for many practical purposes
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