Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knapsack problems in products of groups   The classic knapsack and related problems have natural generalizations to
arbitrary (non-commutative) groups, collectively called knapsack-type problems
in groups. We study the effect of free and direct products on their time
complexity. We show that free products in certain sense preserve time
complexity of knapsack-type problems, while direct products may amplify it. Our
methods allow to obtain complexity results for rational subset membership
problem in amalgamated free products over finite subgroups.

16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th