Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Maximization of Weakly Modular Functions: Guarantees of Multi-stage
  Algorithms, Tractability, and Hardness   Maximization of {\it non-submodular} functions appears in various scenarios,
and many previous works studied it based on some measures that quantify the
closeness to being submodular. On the other hand, many practical non-submodular
functions are actually close to being {\it modular}, which has been utilized in
few studies. In this paper, we study cardinality-constrained maximization of
{\it weakly modular} functions, whose closeness to being modular is measured by
{\it submodularity} and {\it supermodularity ratios}, and reveal what we can
and cannot do by using the weak modularity. We first show that guarantees of
multi-stage algorithms can be proved with the weak modularity, which generalize
and improve some existing results, and experiments confirm their effectiveness.
We then show that weakly modular maximization is {\it fixed-parameter
tractable} under certain conditions; as a byproduct, we provide a new
time--accuracy trade-off for $\ell_0$-constrained minimization. We finally
prove that, even if objective functions are weakly modular, no polynomial-time
algorithms can improve the existing approximation guarantees achieved by the
greedy algorithm.

15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
2
The categories of this paper are: math