Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scheduling of unit-length jobs with cubic incompatibility graphs on
  three uniform machines   In the paper we consider the problem of scheduling $n$ identical jobs on 3
uniform machines with speeds $s_1, s_2,$ and $s_3$ to minimize the schedule
length. We assume that jobs are subjected to some kind of mutual exclusion
constraints, modeled by a cubic incompatibility graph. We show that if the
graph is 2-chromatic then the problem can be solved in $O(n^2)$ time. If the
graph is 3-chromatic, the problem becomes NP-hard even if $s_1>s_2=s_3$.
However, in this case there exists a $4/3$-approximation algorithm running in
$O(n^3)$ time. Moreover, this algorithm solves the problem almost surely to
optimality if $3s_1/4 \leq s_2 = s_3$.

15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph