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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Journal ArticleDOI
Popular Matchings
TL;DR: The first polynomial-time algorithms to determine if an instance admits a popular matching, and to find a largest such matching, if one exists are given.
Proceedings ArticleDOI
Popular matchings
TL;DR: In this article, the problem of determining if an instance admits a popular matching, and to find a largest such matching, if one exists, was studied, and the first polynomial-time algorithms were given.
Proceedings ArticleDOI
Rank-maximal matchings
TL;DR: In this article, the Hungarian algorithm is used to compute a greedy matching in a bipartite graph G = (A U P,e), where e consists of all pairs (a, p) such that post p appears in the preference list of applicant a.
Journal ArticleDOI
Rank-maximal matchings
TL;DR: In this paper, a rank-maximal matching algorithm was proposed to compute a matching with running time O(min(n p C,C √n)m, where C is the maximal rank of an edge used in a rankmaximal match, n is the number of applicants and posts, and m is the total size of the preference lists.
Book ChapterDOI
Popular matchings in the capacitated house allocation problem
David F. Manlove,Colin T. S. Sng +1 more
TL;DR: An O(√Cn 1 + m) algorithm is given to determine if an instance of CHA admits a popular matching, and if so, to find a largest such matching, where C is thetotal capacity of the houses, n 1 is the number of agents and m is the total length of the agents' preference lists.