Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shortest Reconfiguration Sequence for Sliding Tokens on Spiders   Suppose that two independent sets $I$ and $J$ of a graph with $\vert I \vert
= \vert J \vert$ are given, and a token is placed on each vertex in $I$. The
Sliding Token problem is to determine whether there exists a sequence of
independent sets which transforms $I$ into $J$ so that each independent set in
the sequence results from the previous one by sliding exactly one token along
an edge in the graph. It is one of the representative reconfiguration problems
that attract the attention from the viewpoint of theoretical computer science.
For a yes-instance of a reconfiguration problem, finding a shortest
reconfiguration sequence has a different aspect. In general, even if it is
polynomial time solvable to decide whether two instances are reconfigured with
each other, it can be $\mathsf{NP}$-hard to find a shortest sequence between
them. In this paper, we show that the problem for finding a shortest sequence
between two independent sets is polynomial time solvable for spiders (i.e.,
trees having exactly one vertex of degree at least three).

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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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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: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: hep-ex