Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On The Parameterized Tractability of the Just-In-Time Flow-Shop
  Scheduling Problem   Since its development in the early 90's, parameterized complexity has been
widely used to analyze the tractability of many NP-hard combinatorial
optimization problems with respect to various types of problem parameters.
While the generic nature of the framework allows the analysis of any
combinatorial problem, the main focus along the years was on analyzing graph
problems. In this paper we diverge from this trend by studying the
parameterized complexity of Just-In-Time (JIT) flow-shop scheduling problems.
Our analysis focuses on the case where the number of due dates is considerably
smaller than the number of jobs, and can thus be considered as a parameter. We
prove that the two-machine problem is W[1]-hard with respect to this parameter,
even if all processing times on the second machine are of unit length, while
the problem is in XP even for a parameterized number of machines. We then move
on to study the tractability of the problem when combining the different number
of due dates with either the number of different weights or the number of
different processing times on the first machine. We prove that in both cases
the problem is fixed-parameter tractable for the two machine case, and is
W[1]-hard for three or more machines.

22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
9
The categories of this paper are: nlin