# Characterisation of Strongly Stable Matchings

@inproceedings{Kunysz2015CharacterisationOS,
title={Characterisation of Strongly Stable Matchings},
author={Adam Kunysz and Katarzyna E. Paluch and Pratik Ghosal},
booktitle={ACM-SIAM Symposium on Discrete Algorithms},
year={2015}
}
• Published in
ACM-SIAM Symposium on…
1 June 2015
• Mathematics
An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph G = (A∪B, E), with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given vertex. Ties are disjoint and may contain one vertex. A matching M is a set of vertex-disjoint edges. An edge (x, y) ∈ E\M is a blocking edge for M if x is either unmatched or strictly prefers y to its current partner in M, and y is either unmatched or strictly…
12 Citations
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• 2021
A polyhedral characterisation of the set of allsuper-stable matchings is given and it is proved that the super-stable matching polytope is integral, thus solving an open problem stated in the book by Gusfield and Irving.
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The main result of this paper is an efficient O(nm log (Wn) time algorithm for computing a maximum weight strongly stable matching, where n = |V |, m = |E| and W is amaximum weight of an edge in G, which shows that the problem can be solved in O (nm) time.
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This work employs the theory of rotations for Stable Roommates to develop a polynomial-time algorithm for adapting StableRoommates matchings to forced pairs and shows that the same problem for forbidden pairs is NP-hard.
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When computing stable matchings, it is usually assumed that the preferences of the agents in the matching market are fixed. However, in many realistic scenarios, preferences change over time.
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2019 10th International Conference on Computing, Communication and Networking Technologies (ICCCNT)
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An algorithm is proposed to rank the choices of a tenant or house owner by the preferences they desire, used here for the matching between the tenants and house owners so that there will be no unstable tenant-owner pair.
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This work investigates two extensions introduced in this framework -- legal assignments and the EADAM algorithm -- through the lens of classical theory of stable matchings, and proves that the set ${\cal L}$ is exactly the set of stable assignments in another instance.