Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability-Preserving, Time-Efficient Mechanisms for School Choice in Two
  Rounds   We address the following dynamic version of the school choice question: a
city, named City, admits students in two temporally-separated rounds, denoted
$\mathcal{R}_1$ and $\mathcal{R}_2$. In round $\mathcal{R}_1$, the capacity of
each school is fixed and mechanism $\mathcal{M}_1$ finds a student optimal
stable matching. In round $\mathcal{R}_2$, certain parameters change, e.g., new
students move into the City or the City is happy to allocate extra seats to
specific schools. We study a number of Settings of this kind and give
polynomial time algorithms for obtaining a stable matching for the new
situations.
  It is well established that switching the school of a student midway,
unsynchronized with her classmates, can cause traumatic effects. This fact
guides us to two types of results, the first simply disallows any
re-allocations in round $\mathcal{R}_2$, and the second asks for a stable
matching that minimizes the number of re-allocations. For the latter, we prove
that the stable matchings which minimize the number of re-allocations form a
sublattice of the lattice of stable matchings. Observations about incentive
compatibility are woven into these results. We also give a third type of
results, namely proofs of NP-hardness for a mechanism for round $\mathcal{R}_2$
under certain settings.

10
The categories of this paper are: q-bio
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc