Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Super-stability in the Student-Project Allocation Problem with Ties   The Student-Project Allocation problem with lecturer preferences over
Students (SPA-S) involves assigning students to projects based on student
preferences over projects, lecturer preferences over students, and the maximum
number of students that each project and lecturer can accommodate. This
classical model assumes that each project is offered by one lecturer and that
preference lists are strictly ordered. Here, we study a generalisation of SPA-S
where ties are allowed in the preference lists of students and lecturers, which
we refer to as the Student-Project Allocation problem with lecturer preferences
over Students with Ties (SPA-ST). We investigate stable matchings under the
most robust definition of stability in this context, namely super-stability. We
describe the first polynomial-time algorithm to find a super-stable matching or
to report that no such matching exists, given an instance of SPA-ST. Our
algorithm runs in $O(L)$ time, where $L$ is the total length of all the
preference lists. Finally, we present results obtained from an empirical
evaluation of the linear-time algorithm based on randomly-generated SPA-ST
instances. Our main finding is that, whilst super-stable matchings can be
elusive when ties are present in the students' and lecturers' preference lists,
the probability of such a matching existing is significantly higher if ties are
restricted to the lecturers' preference lists.

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The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
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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: nlin
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn