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- W2904683578 abstract "A stable matching instance $A$ is transmitted over a channel which introduces {em one error} from a super-exponentially large set, $T$; the error consists of arbitrarily permuting the preference list of any one boy or any one girl. An arbitrary set $S subseteq T$ is specified. We give an $O(|S| p(n))$ time algorithm for finding a matching that is stable for $A$ and for each of the $|S|$ instances that result by introducing one error from $S$, where $p$ is a polynomial function. In particular, if $S$ is polynomial sized, then our algorithm runs in polynomial time. Our algorithm is based on new, non-trivial structural properties of the lattice of stable matchings. A second ingredient of our algorithm is a generalization of Birkhoff's Theorem for finite distributive lattices which states that corresponding to such a lattice, $mathcal{L}$, there is a partial order, say $Pi$, such that the lattice of closed sets of $Pi$, $L(Pi)$, is isomorphic to $mathcal{L}$. Our generalization shows that corresponding to each sublattice $mathcal{L}'$ of $mathcal{L}$, there is a partial order $Pi'$ that can be obtained from $Pi$ (via a specified operation) such that $L(Pi') cong mathcal{L}'$. This generalization is of independent interest." @default.
- W2904683578 created "2018-12-22" @default.
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- W2904683578 date "2018-04-16" @default.
- W2904683578 modified "2023-09-27" @default.
- W2904683578 title "Stable Matchings, Robust Solutions, and Distributive Lattices" @default.
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