Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed Reconfiguration of Maximal Independent Sets   In this paper, we investigate a distributed maximal independent set (MIS)
reconfiguration problem, in which there are two maximal independent sets for
which every node is given its membership status, and the nodes need to
communicate with their neighbors in order to find a reconfiguration schedule
that switches from the first MIS to the second. Such a schedule is a list of
independent sets that is restricted by forbidding two neighbors to change their
membership status at the same step. In addition, these independent sets should
provide some covering guarantee. We show that obtaining an actual MIS (and even
a 3-dominating set) in each intermediate step is impossible. However, we
provide efficient solutions when the intermediate sets are only required to be
independent and 4-dominating, which is almost always possible, as we fully
characterize. Consequently, our goal is to pin down the tradeoff between the
possible length of the schedule and the number of communication rounds. We
prove that a constant length schedule can be found in
$O(\texttt{MIS}+\texttt{R32})$ rounds, where $\texttt{MIS}$ is the complexity
of finding an MIS in a worst-case graph and $\texttt{R32}$ is the complexity of
finding a $(3,2)$-ruling set. For bounded degree graphs, this is $O(\log^*n)$
rounds and we show that it is necessary. On the other extreme, we show that
with a constant number of rounds we can find a linear length schedule.

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The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin