Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On semi-discrete Monge problem and generalized optimal partitions   Let $X$ a probability measure space and $\psi_1....\psi_N$ measurable, real
valued functions on $X$. Consider all possible partitions of $X$ into $N$
disjoint subdomains $X_i$ on which $\int_{X_i}\psi_i$ are prescribed. We
address the question of characterizing the set $(m_1,,,m_N) \in R^N$ for which
there exists a partition $X_1, ...X_N$ of $X$ satisfying $\int_{X_i}\psi_i=
m_i$ and discuss some optimization problems on this set of partitions. The
relation of this problem to semi-discrete version of optimal mass
transportation is discussed as well.

3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph