Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Posimodular Function Optimization   Given a posimodular function $f: 2^V \to \mathbb{R}$ on a finite set $V$, we
consider the problem of finding a nonempty subset $X$ of $V$ that minimizes
$f(X)$. Posimodular functions often arise in combinatorial optimization such as
undirected cut functions. In this paper, we show that any algorithm for the
problem requires $\Omega(2^{\frac{n}{7.54}})$ oracle calls to $f$, where
$n=|V|$. It contrasts to the fact that the submodular function minimization,
which is another generalization of cut functions, is polynomially solvable.
  When the range of a given posimodular function is restricted to be
$D=\{0,1,...,d\}$ for some nonnegative integer $d$, we show that
$\Omega(2^{\frac{d}{15.08}})$ oracle calls are necessary, while we propose an
$O(n^dT_f+n^{2d+1})$-time algorithm for the problem. Here, $T_f$ denotes the
time needed to evaluate the function value $f(X)$ for a given $X \subseteq V$.
  We also consider the problem of maximizing a given posimodular function. We
show that $\Omega(2^{n-1})$ oracle calls are necessary for solving the problem,
and that the problem has time complexity $\Theta(n^{d-1}T_f) $ when
$D=\{0,1,..., d\}$ is the range of $f$ for some constant $d$.

9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol