Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved Distributed Lower Bounds for MIS and Bounded (Out-)Degree
  Dominating Sets in Trees   Recently, Balliu, Brandt, and Olivetti [FOCS '20] showed the first
$\omega(\log^* n)$ lower bound for the maximal independent set (MIS) problem in
trees. In this work we prove lower bounds for a much more relaxed family of
distributed symmetry breaking problems. As a by-product, we obtain improved
lower bounds for the distributed MIS problem in trees.
  For a parameter $k$ and an orientation of the edges of a graph $G$, we say
that a subset $S$ of the nodes of $G$ is a $k$-outdegree dominating set if $S$
is a dominating set of $G$ and if in the induced subgraph $G[S]$, every node in
$S$ has outdegree at most $k$. Note that for $k=0$, this definition coincides
with the definition of an MIS. For a given $k$, we consider the problem of
computing a $k$-outdegree dominating set. We show that, even in regular trees
of degree at most $\Delta$, in the standard \LOCAL model, there exists a
constant $\epsilon>0$ such that for $k\leq \Delta^\epsilon$, for the problem of
computing a $k$-outdegree dominating set, any randomized algorithm requires at
least $\Omega(\min\{\log\Delta,\sqrt{\log\log n}\})$ rounds and any
deterministic algorithm requires at least $\Omega(\min\{\log\Delta,\sqrt{\log
n}\})$ rounds.
  The proof of our lower bounds is based on the recently highly successful
round elimination technique. We provide a novel way to do simplifications for
round elimination, which we expect to be of independent interest. Our new proof
is considerably simpler than the lower bound proof in [FOCS '20]. In
particular, our round elimination proof uses a family of problems that can be
described by only a constant number of labels. The existence of such a proof
for the MIS problem was believed impossible by the authors of [FOCS '20].

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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci