Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity of the FIFO Stack-Up Problem   We study the combinatorial FIFO stack-up problem. In delivery industry, bins
have to be stacked-up from conveyor belts onto pallets with respect to customer
orders. Given k sequences q_1, ..., q_k of labeled bins and a positive integer
p, the aim is to stack-up the bins by iteratively removing the first bin of one
of the k sequences and put it onto an initially empty pallet of unbounded
capacity located at one of p stack-up places. Bins with different pallet labels
have to be placed on different pallets, bins with the same pallet label have to
be placed on the same pallet. After all bins for a pallet have been removed
from the given sequences, the corresponding stack-up place will be cleared and
becomes available for a further pallet. The FIFO stack-up problem is to find a
stack-up sequence such that all pallets can be build-up with the available p
stack-up places. In this paper, we introduce two digraph models for the FIFO
stack-up problem, namely the processing graph and the sequence graph. We show
that there is a processing of some list of sequences with at most p stack-up
places if and only if the sequence graph of this list has directed pathwidth at
most p-1. This connection implies that the FIFO stack-up problem is NP-complete
in general, even if there are at most 6 bins for every pallet and that the
problem can be solved in polynomial time, if the number p of stack-up places is
assumed to be fixed. Further the processing graph allows us to show that the
problem can be solved in polynomial time, if the number k of sequences is
assumed to be fixed.

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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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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: hep-th
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The categories of this paper are: cmp-lg