Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tight Analysis of Randomized Greedy MIS   We provide a tight analysis which settles the round complexity of the
well-studied parallel randomized greedy MIS algorithm, thus answering the main
open question of Blelloch, Fineman, and Shun [SPAA'12].
  The parallel/distributed randomized greedy Maximal Independent Set (MIS)
algorithm works as follows. An order of the vertices is chosen uniformly at
random. Then, in each round, all vertices that appear before their neighbors in
the order are added to the independent set and removed from the graph along
with their neighbors. The main question of interest is the number of rounds it
takes until the graph is empty. This algorithm has been studied since 1987,
initiated by Coppersmith, Raghavan, and Tompa [FOCS'87], and the previously
best known bounds were $O(\log n)$ rounds in expectation for
Erd\H{o}s-R\'{e}nyi random graphs by Calkin and Frieze [Random Struc. \& Alg.
'90] and $O(\log^2 n)$ rounds with high probability for general graphs by
Blelloch, Fineman, and Shun [SPAA'12].
  We prove a high probability upper bound of $O(\log n)$ on the round
complexity of this algorithm in general graphs, and that this bound is tight.
This also shows that parallel randomized greedy MIS is as fast as the
celebrated algorithm of Luby [STOC'85, JALG'86].

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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: econ
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat