Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial separation algorithms for the continuous knapsack
  polyhedra with divisible capacities   It is important to design separation algorithms of low computational
complexity in mixed integer programming. We study the separation problems of
the two continuous knapsack polyhedra with divisible capacities. The two
polyhedra are the convex hulls of the sets which consist of $ n $ nonnegative
integer variables, one unbounded continuous, $ m $ bounded continuous
variables, and one linear constraint in either $ \geq $ or $ \leq $ form where
the coefficients of integer variables are integer and divisible. Wolsey and
Yaman (Math Program 156: 1--20, 2016) have shown that the polyhedra can be
described by adding the two closely related families of partition inequalities.
However, no combinatorial separation algorithm is known yet for the polyhedra.
In this paper, for each polyhedron, we provide a combinatorial separation
algorithm with the complexity of $ \mathcal{O}(nm+m\log m ) $. In particular,
we solve the separation problem for the continuous $ \geq $-knapsack polyhedron
by presenting a polynomial-time separation algorithm for the family of $ \geq
$-partition inequalities. For the continuous $ \leq $-knapsack polyhedron, we
derive the complemented partition inequalities, which dominate the $ \leq
$-partition inequalities. The continuous $ \leq $-knapsack polyhedron is
completely described with the addition of the proposed inequalities. We again
show that the family of the proposed inequalities can be separated in
polynomial time.

11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: stat
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat