Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Approach to Online Scheduling: Approximating the Optimal
  Competitive Ratio   We propose a new approach to competitive analysis in online scheduling by
introducing the novel concept of competitive-ratio approximation schemes. Such
a scheme algorithmically constructs an online algorithm with a competitive
ratio arbitrarily close to the best possible competitive ratio for any online
algorithm. We study the problem of scheduling jobs online to minimize the
weighted sum of completion times on parallel, related, and unrelated machines,
and we derive both deterministic and randomized algorithms which are almost
best possible among all online algorithms of the respective settings. We also
generalize our techniques to arbitrary monomial cost functions and apply them
to the makespan objective. Our method relies on an abstract characterization of
online algorithms combined with various simplifications and transformations. We
also contribute algorithmic means to compute the actual value of the best
possi- ble competitive ratio up to an arbitrary accuracy. This strongly
contrasts all previous manually obtained competitiveness results for algorithms
and, most importantly, it reduces the search for the optimal com- petitive
ratio to a question that a computer can answer. We believe that our concept can
also be applied to many other problems and yields a new perspective on online
algorithms in general.

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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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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: quant-ph
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The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con