Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Minimization of Higher Order Submodular Functions using
  Monotonic Boolean Functions   Submodular function minimization is a key problem in a wide variety of
applications in machine learning, economics, game theory, computer vision, and
many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4
{\log}^{O(1)} n)$ where $E$ is the time required to evaluate the function and
$n$ is the number of variables \cite{Lee2015}. On the other hand, many computer
vision and machine learning problems are defined over special subclasses of
submodular functions that can be written as the sum of many submodular cost
functions defined over cliques containing few variables. In such functions, the
pseudo-Boolean (or polynomial) representation \cite{BorosH02} of these
subclasses are of degree (or order, or clique size) $k$ where $k \ll n$. In
this work, we develop efficient algorithms for the minimization of this useful
subclass of submodular functions. To do this, we define novel mapping that
transform submodular functions of order $k$ into quadratic ones. The underlying
idea is to use auxiliary variables to model the higher order terms and the
transformation is found using a carefully constructed linear program. In
particular, we model the auxiliary variables as monotonic Boolean functions,
allowing us to obtain a compact transformation using as few auxiliary variables
as possible.

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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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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: hep-ph
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The categories of this paper are: math
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat