Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Pseudo-Polynomial Factor Algorithm for Automaton Constrained Tree
  Knapsack Problem   The automaton constrained tree knapsack problem is a variant of the knapsack
problem in which the items are associated with the vertices of the tree, and we
can select a subset of items that is accepted by a top-down tree automaton. If
the capacities or the profits of items are integers, the problem can be solved
in pseudo-polynomial time using the dynamic programming algorithm. However, the
natural implementation of this algorithm has a quadratic pseudo-polynomial
factor in its complexity because of the max-plus convolution. In this study, we
propose a new dynamic programming technique, called \emph{heavy-light recursive
dynamic programming}, to obtain pseudo-polynomial time algorithms having linear
pseudo-polynomial factors in the complexity. Such algorithms can be used for
solving the problems with polynomially small capacities/profits efficiently,
and used for deriving efficient fully polynomial-time approximation schemes. We
also consider the $k$-subtree version problem that finds $k$ disjoint subtrees
and a solution in each subtree that maximizes total profit under a budget
constraint. We show that this problem can be solved in almost the same order as
the original problem.

3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph