Book ChapterDOI
Classified Rank-Maximal Matchings and Popular Matchings – Algorithms and Hardness
Meghana Nasre,Prajakta Nimbhorkar,Nada Pulath +2 more
- pp 244-257
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TLDR
This paper considers the problem of computing an optimal matching in a bipartite graph where elements of A specify preferences over their neighbors in P, possibly involving ties, and each vertex can have capacities and classifications.Abstract:
In this paper, we consider the problem of computing an optimal matching in a bipartite graph \(G=(A\cup P, E)\) where elements of A specify preferences over their neighbors in P, possibly involving ties, and each vertex can have capacities and classifications. A classification \(\mathcal {C}_u\) for a vertex u is a collection of subsets of neighbors of u. Each subset (class) \(C\in \mathcal {C}_u\) has an upper quota denoting the maximum number of vertices from C that can be matched to u. The goal is to find a matching that is optimal amongst all the feasible matchings, which are matchings that respect quotas of all the vertices and classes.read more
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Journal Article
Popular Matchings with Ties and Matroid Constraints
Naoyuki Kamiyama,直之 神山 +1 more
TL;DR: In this paper, a set of applicants and posts such that each applicant has a preference list over the posts is given, and a matching $M$ between the applicants and the posted posts is said to be a popu...
Rank-Maximal Matchings
TL;DR: An algorithm is given to compute a rank-maximal matching with running time O(min(n + C,C &sqrt;n)m), where n is the number of applicants and posts and m is the total size of the preference lists.
Journal ArticleDOI
Bipartite Matchings with Group Fairness and Individual Fairness Constraints
TL;DR: This work addresses group as well as individual fairness constraints in matchings in the context of assigning items to platforms by providing a polynomial-time algorithm that computes a probabilistic individually fair distribution over group fair matchings.
Proceedings ArticleDOI
Optimal Matchings with One-Sided Preferences: Fixed and Cost-Based Quotas
TL;DR: This work considers the well-studied many-to-one bipartite matching problem of assigning applicants A to posts P where applicants rank posts in the order of preference and proposes a novel optimality criterion, which is called the “cumulative better signature”.
Individual fairness under Varied Notions of Group Fairness in Bipartite Matching -- One Framework to Approximate Them Al
TL;DR: In this paper , the authors consider the problem of assigning items to platforms while satisfying group and individual fairness constraints, and provide a polynomial-time algorithm that computes a probabilistic individually fair distribution over group fair matching.
References
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Book ChapterDOI
Weighted popular matchings
TL;DR: This work presents two algorithms to find a popular matching, or in case none exists, to establish so, and develops an O(n+m) time algorithm for the case of strict preferences.
Journal ArticleDOI
A matroid approach to stable matchings with lower quotas
TL;DR: A matroid-based approach to the laminar classified stable matching problem (LCSM) is proposed and it is proved that the set of stable assignments of the LCSM problem has a lattice structure similarly to the ordinary stable matching model.
Proceedings ArticleDOI
Classified stable matching
TL;DR: In this article, a stable matching problem motivated by academic hiring is introduced, where a number of institutes are hiring faculty members from a pool of applicants, and both institutes and applicants have preferences over the other side.
Journal ArticleDOI
Bounded Unpopularity Matchings
TL;DR: Simulation results suggest that the algorithm finds a matching with low unpopularity in random instances after considering two measures of unpopularity—unpopularity factor and unpopularity margin.
Book ChapterDOI
Capacitated Rank-Maximal Matchings
TL;DR: A combinatorial algorithm for the capacitated version of the rank-maximal matching problem, in which each applicant or post v has capacity b(v), which is based on a weakly polynomial algorithm of Gabow and Tarjan using scaling.