Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An O(m^2 log m)-Competitive Algorithm for Online Machine Minimization   We consider the online machine minimization problem in which jobs with hard
deadlines arrive online over time at their release dates. The task is to
determine a feasible schedule on a minimum number of machines. Our main result
is a general O(m^2 log m)-competitive algorithm for the preemptive online
problem, where m is the optimal number of machines used in an offline solution.
This is the first improvement on an O(log (p_max/p_min))-competitive algorithm
by Phillips et al. (STOC 1997), which was to date the best known algorithm even
when m=2. Our algorithm is O(1)-competitive for any m that is bounded by a
constant. To develop the algorithm, we investigate two complementary special
cases of the problem, namely, laminar instances and agreeable instances, for
which we provide an O(log m)-competitive and an O(1)-competitive algorithm,
respectively. Our O(1)-competitive algorithm for agreeable instances actually
produces a non-preemptive schedule, which is of its own interest as there
exists a strong lower bound of n, the number of jobs, for the general
non-preemptive online machine minimization problem by Saha (FSTTCS 2013), which
even holds for laminar instances.

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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: physics