Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flow Time Scheduling and Prefix Beck-Fiala   We relate discrepancy theory with the classic scheduling problems of
minimizing max flow time and total flow time on unrelated machines.
Specifically, we give a general reduction that allows us to transfer
discrepancy bounds in the prefix Beck-Fiala (bounded $\ell_1$-norm) setting to
bounds on the flow time of an optimal schedule.
  Combining our reduction with a deep result proved by Banaszczyk via convex
geometry, give guarantees of $O(\sqrt{\log n})$ and $O(\sqrt{\log n} \log P)$
for max flow time and total flow time, respectively, improving upon the
previous best guarantees of $O(\log n)$ and $O(\log n \log P)$. Apart from the
improved guarantees, the reduction motivates seemingly easy versions of prefix
discrepancy questions: any constant bound on prefix Beck-Fiala where vectors
have sparsity two (sparsity one being trivial) would already yield tight
guarantees for both max flow time and total flow time. While known techniques
solve this case when the entries take values in $\{-1,0,1\}$, we show that they
are unlikely to transfer to the more general $2$-sparse case of bounded
$\ell_1$-norm.

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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
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The categories of this paper are: adap-org
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th