Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Solving Cycle Problems with Branch-and-Cut: Extending Shrinking and
  Exact Subcycle Elimination Separation Algorithms   In this paper, we extend techniques developed in the context of the
Travelling Salesperson Problem for cycle problems. Particularly, we study the
shrinking of support graphs and the exact algorithms for subcycle elimination
separation problems. The efficient application of the considered techniques has
proved to be essential in the Travelling Salesperson Problem when solving large
size problems by Branch-and-Cut, and this has been the motivation behind this
work. Regarding the shrinking of support graphs, we prove the validity of the
Padberg-Rinaldi general shrinking rules and the Crowder-Padberg subcycle-safe
shrinking rules. Concerning the subcycle separation problems, we extend two
exact separation algorithms, the Dynamic Hong and the Extended
Padberg-Gr\"otschel algorithms, which are shown to be superior to the ones used
so far in the literature of cycle problems.
  The proposed techniques are empirically tested in 24 subcycle elimination
problem instances generated by solving the Orienteering Problem (involving up
to 15112 vertices) with Branch-and-Cut. The experiments suggest the relevance
of the proposed techniques for cycle problems. The obtained average speedup for
the subcycle separation problems in the Orienteering Problem when the proposed
techniques are used together is around 50 times in medium-sized instances and
around 250 times in large-sized instances.

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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg