Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Profile-based optimal matchings in the Student/Project Allocation
  problem   In the Student / Project Allocation problem (SPA) we seek to assign students
to individual or group projects offered by lecturers. Students provide a list
of projects they find acceptable in order of preference. Each student can be
assigned to at most one project and there are constraints on the maximum number
of students that can be assigned to each project and lecturer. We seek
matchings of students to projects that are optimal with respect to profile,
which is a vector whose rth component indicates how many students have their
rth-choice project. We present an efficient algorithm for finding a greedy
maximum matching in the SPA context - this is a maximum matching whose profile
is lexicographically maximum. We then show how to adapt this algorithm to find
a generous maximum matching - this is a matching whose reverse profile is
lexicographically minimum. Our algorithms involve finding optimal flows in
networks. We demonstrate how this approach can allow for additional
constraints, such as lecturer lower quotas, to be handled flexibly. Finally we
present results obtained from an empirical evaluation of the algorithms.

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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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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: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: physics