Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Randomized Composable Core-sets for Distributed Submodular Maximization   An effective technique for solving optimization problems over massive data
sets is to partition the data into smaller pieces, solve the problem on each
piece and compute a representative solution from it, and finally obtain a
solution inside the union of the representative solutions for all pieces. This
technique can be captured via the concept of {\em composable core-sets}, and
has been recently applied to solve diversity maximization problems as well as
several clustering problems. However, for coverage and submodular maximization
problems, impossibility bounds are known for this technique \cite{IMMM14}. In
this paper, we focus on efficient construction of a randomized variant of
composable core-sets where the above idea is applied on a {\em random
clustering} of the data. We employ this technique for the coverage, monotone
and non-monotone submodular maximization problems. Our results significantly
improve upon the hardness results for non-randomized core-sets, and imply
improved results for submodular maximization in a distributed and streaming
settings.
  In summary, we show that a simple greedy algorithm results in a
$1/3$-approximate randomized composable core-set for submodular maximization
under a cardinality constraint. This is in contrast to a known $O({\log k\over
\sqrt{k}})$ impossibility result for (non-randomized) composable core-set. Our
result also extends to non-monotone submodular functions, and leads to the
first 2-round MapReduce-based constant-factor approximation algorithm with
$O(n)$ total communication complexity for either monotone or non-monotone
functions. Finally, using an improved analysis technique and a new algorithm
$\mathsf{PseudoGreedy}$, we present an improved $0.545$-approximation algorithm
for monotone submodular maximization, which is in turn the first
MapReduce-based algorithm beating factor $1/2$ in a constant number of rounds.

2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th