Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scheduling to Approximate Minimization Objectives on Identical Machines   This paper considers scheduling on identical machines. The scheduling
objective considered in this paper generalizes most scheduling minimization
problems. In the problem, there are $n$ jobs and each job $j$ is associated
with a monotonically increasing function $g_j$. The goal is to design a
schedule that minimizes $\sum_{j \in [n]} g_{j}(C_j)$ where $C_j$ is the
completion time of job $j$ in the schedule. An $O(1)$-approximation is known
for the single machine case. On multiple machines, this paper shows that if the
scheduler is required to be either non-migratory or non-preemptive then any
algorithm has an unbounded approximation ratio. Using preemption and migration,
this paper gives a $O(\log \log nP)$-approximation on multiple machines, the
first result on multiple machines. These results imply the first non-trivial
positive results for several special cases of the problem considered, such as
throughput minimization and tardiness.
  Natural linear programs known for the problem have a poor integrality gap.
The results are obtained by strengthening a natural linear program for the
problem with a set of covering inequalities we call job cover inequalities.
This linear program is rounded to an integral solution by building on
quasi-uniform sampling and rounding techniques.

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The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
2
The categories of this paper are: math
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The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys