Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Doing-it-All with Bounded Work and Communication   We consider the Do-All problem, where $p$ cooperating processors need to
complete $t$ similar and independent tasks in an adversarial setting. Here we
deal with a synchronous message passing system with processors that are subject
to crash failures. Efficiency of algorithms in this setting is measured in
terms of work complexity (also known as total available processor steps) and
communication complexity (total number of point-to-point messages). When work
and communication are considered to be comparable resources, then the overall
efficiency is meaningfully expressed in terms of effort defined as work +
communication. We develop and analyze a constructive algorithm that has work
$O( t + p \log p\, (\sqrt{p\log p}+\sqrt{t\log t}\, ) )$ and a nonconstructive
algorithm that has work $O(t +p \log^2 p)$. The latter result is close to the
lower bound $\Omega(t + p \log p/ \log \log p)$ on work. The effort of each of
these algorithms is proportional to its work when the number of crashes is
bounded above by $c\,p$, for some positive constant $c < 1$. We also present a
nonconstructive algorithm that has effort $O(t + p ^{1.77})$.

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The categories of this paper are: cond-mat
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: math
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The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg