Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on Submodular Maximization over Independence Systems   In this work, we consider the maximization of submodular functions
constrained by independence systems. Because of the wide applicability of
submodular functions, this problem has been extensively studied in the
literature, on specialized independence systems. For general independence
systems, even when all of the bases of the independence system have the same
size, we show that for any $\epsilon > 0$, the problem is hard to approximate
within $(2/n)^{1-\epsilon}$, where $n$ is the size of the ground set. In the
same context, we show the greedy algorithm does obtain a ratio of $2/n$ under
an additional mild additional assumption. Finally, we provide the first nearly
linear-time algorithm for maximization of non-monotone submodular functions
over $p$-extendible independence systems.

29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin