Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal proper non-IRUP instances of the one-dimensional Cutting Stock
  Problem   We consider the well-known one dimensional cutting stock problem (1CSP).
Based on the pattern structure of the classical ILP formulation of Gilmore and
Gomory, we can decompose the infinite set of 1CSP instances, with a fixed
demand n, into a finite number of equivalence classes. We show up a strong
relation to weighted simple games. Studying the integer round-up property we
computationally show that all 1CSP instances with $n\le 9$ are proper IRUP,
while we give examples of a proper non-IRUP instances with $n=10$. A gap larger
than 1 occurs for $n=11$. The worst known gap is raised from 1.003 to 1.0625.
The used algorithmic approaches are based on exhaustive enumeration and integer
linear programming. Additionally we give some theoretical bounds showing that
all 1CSP instances with some specific parameters have the proper IRUP.

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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: cs