Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized roof duality and bisubmodular functions   Consider a convex relaxation $\hat f$ of a pseudo-boolean function $f$. We
say that the relaxation is {\em totally half-integral} if $\hat f(x)$ is a
polyhedral function with half-integral extreme points $x$, and this property is
preserved after adding an arbitrary combination of constraints of the form
$x_i=x_j$, $x_i=1-x_j$, and $x_i=\gamma$ where $\gamma\in\{0, 1, 1/2}$ is a
constant. A well-known example is the {\em roof duality} relaxation for
quadratic pseudo-boolean functions $f$. We argue that total half-integrality is
a natural requirement for generalizations of roof duality to arbitrary
pseudo-boolean functions. Our contributions are as follows. First, we provide a
complete characterization of totally half-integral relaxations $\hat f$ by
establishing a one-to-one correspondence with {\em bisubmodular functions}.
Second, we give a new characterization of bisubmodular functions. Finally, we
show some relationships between general totally half-integral relaxations and
relaxations based on the roof duality.

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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: math
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org