Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive Greedy versus Non-adaptive Greedy for Influence Maximization   We consider the \emph{adaptive influence maximization problem}: given a
network and a budget $k$, iteratively select $k$ 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 $(1-1/e)$-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 $(1-1/e)$ 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 $(1-1/e)$-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.

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The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn