Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Branch and Cut Algorithm for the Halfspace Depth Problem   The concept of data depth in non-parametric multivariate descriptive
statistics is the generalization of the univariate rank method to multivariate
data. Halfspace depth is a measure of data depth. Given a set S of points and a
point p, the halfspace depth (or rank) k of p is defined as the minimum number
of points of S contained in any closed halfspace with p on its boundary.
Computing halfspace depth is NP-hard, and it is equivalent to the Maximum
Feasible Subsystem problem. In this thesis a mixed integer program is
formulated with the big-M method for the halfspace depth problem. We suggest a
branch and cut algorithm. In this algorithm, Chinneck's heuristic algorithm is
used to find an upper bound and a related technique based on sensitivity
analysis is used for branching. Irreducible Infeasible Subsystem (IIS) hitting
set cuts are applied. We also suggest a binary search algorithm which may be
more stable numerically. The algorithms are implemented with the BCP framework
from the COIN-OR project.

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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th