Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Assignment via Submodular Optimization with Reserved
  Capacity   We study a variant of the \emph{generalized assignment problem} ({\sf GAP})
with group constraints. An instance of {\sf Group GAP} is a set $I$ of items,
partitioned into $L$ groups, and a set of $m$ uniform (unit-sized) bins. Each
item $i \in I$ has a size $s_i >0$, and a profit $p_{i,j} \geq 0$ if packed in
bin $j$. A group of items is \emph{satisfied} if all of its items are packed.
The goal is to find a feasible packing of a subset of the items in the bins
such that the total profit from satisfied groups is maximized. We point to
central applications of {\sf Group GAP} in Video-on-Demand services, mobile
Device-to-Device network caching and base station cooperation in 5G networks.
  Our main result is a $\frac{1}{6}$-approximation algorithm for {\sf Group
GAP} instances where the total size of each group is at most $\frac{m}{2}$. At
the heart of our algorithm lies an interesting derivation of a submodular
function from the classic LP formulation of {\sf GAP}, which facilitates the
construction of a high profit solution utilizing at most half the total bin
capacity, while the other half is \emph{reserved} for later use. In particular,
we give an algorithm for submodular maximization subject to a knapsack
constraint, which finds a solution of profit at least $\frac{1}{3}$ of the
optimum, using at most half the knapsack capacity, under mild restrictions on
element sizes. Our novel approach of submodular optimization subject to a
knapsack \emph{with reserved capacity} constraint may find applications in
solving other group assignment problems.

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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph