Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $b$-bibranching Problem: TDI System, Packing, and Discrete Convexity   In this paper, we introduce the $b$-bibranching problem in digraphs, which is
a common generalization of the bibranching and $b$-branching problems. The
bibranching problem, introduced by Schrijver (1982), is a common generalization
of the branching and bipartite edge cover problems. Previous results on
bibranchings include polynomial algorithms, a linear programming formulation
with total dual integrality, a packing theorem, and an M-convex submodular flow
formulation. The $b$-branching problem, recently introduced by Kakimura,
Kamiyama, and Takazawa (2018), is a generalization of the branching problem
admitting higher indegree, i.e., each vertex $v$ can have indegree at most
$b(v)$. For $b$-branchings, a combinatorial algorithm, a linear programming
formulation with total dual integrality, and a packing theorem for branchings
are extended. A main contribution of this paper is to extend those previous
results on bibranchings and $b$-branchings to $b$-bibranchings. That is, we
present a linear programming formulation with total dual integrality, a packing
theorem, and an M-convex submodular flow formulation for $b$-bibranchings. In
particular, the linear program and M-convex submodular flow formulations
respectively imply polynomial algorithms for finding a shortest
$b$-bibranching.

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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: stat