Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Several methods of analysis for cardinality constrained bin packing   We consider a known variant of bin packing called {\it cardinality
constrained bin packing}, also called {\it bin packing with cardinality
constraints} (BPCC). In this problem, there is a parameter k\geq 2, and items
of rational sizes in [0,1] are to be packed into bins, such that no bin has
more than k items or total size larger than 1. The goal is to minimize the
number of bins.
  A recently introduced concept, called the price of clustering, deals with
inputs that are presented in a way that they are split into clusters. Thus, an
item has two attributes which are its size and its cluster. The goal is to
measure the relation between an optimal solution that cannot combine items of
different clusters into bins, and an optimal solution that can combine items of
different clusters arbitrarily. Usually the number of clusters may be large,
while clusters are relatively small, though not trivially small. Such problems
are related to greedy bin packing algorithms, and to batched bin packing, which
is similar to the price of clustering, but there is a constant number of large
clusters. We analyze the price of clustering for BPCC, including the parametric
case with bounded item sizes. We discuss several greedy algorithms for this
problem that were not studied in the past, and comment on batched bin packing.

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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: patt-sol