Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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
$(1-1/e-\epsilon)$-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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The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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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: alg-geom
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The categories of this paper are: hep-lat