Rank-maximal matchings

Irving, Robert W.; Kavitha, Telikepalli; Mehlhorn, Kurt; Michail, Dimitrios; Paluch, Katarzyna

doi:10.1145/1198513.1198520

Cited by 97 publications

(113 citation statements)

References 5 publications

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“…, σ(A h ) is lexicographically maximum. This objective is closely related the rank-maximal matchings of Irving et al [14] and Mehlhorn and Michail [20], thus its name.…”

Section: An Exact Algorithm For =mentioning

confidence: 98%

“…We show that both problems are NP-hard even when = 3. On the positive side, for = 2 we show that both problems can be solved in polynomial time by establishing a connection to a variant of rank-maximal matchings [14,20]. For larger values of in the case of the weighted preference order we give approximation algorithms building upon ideas of Bezáková and Dani [5], and Shmoys and Tardos [25].…”

Section: (M)) > W(σ R (T ))mentioning

confidence: 99%

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Assigning Papers to Referees

et al. 2010

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Refereed conferences require every submission to be reviewed by members of a program committee (PC) in charge of selecting the conference program. There are many software packages available to manage the review process. Typically, in a bidding phase PC members express their personal preferences by ranking the submissions. This information is used by the system to compute an assignment of the papers to referees (PC members).We study the problem of assigning papers to referees. We propose to optimize a number of criteria that aim at achieving fairness among referees/papers. Some of these variants can be solved optimally in polynomial time, while others are NP-hard, in which case we design approximation algorithms. Experimental results strongly suggest that the assignments computed by our algorithms are considerably better than those computed by popular conference management software.

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“…, σ(A h ) is lexicographically maximum. This objective is closely related the rank-maximal matchings of Irving et al [14] and Mehlhorn and Michail [20], thus its name.…”

Section: An Exact Algorithm For =mentioning

confidence: 98%

Section: (M)) > W(σ R (T ))mentioning

confidence: 99%

Assigning Papers to Referees

et al. 2010

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“…We would now like to contrast our approach above with the approach used in the algorithm for rankmaximal matchings [8]. In the i-th iteration the algorithm for rank-maximal matchings would add edges from an applicant a that is even in each of the previous iterations to a post p that was even in each of the previous iterations if and only if p was a rank i post in a's preference list.…”

Section: Our Algorithmmentioning

confidence: 99%

“…For example, a matching is Paretooptimal [1,3,13] if no applicant can improve his/her allocation (say by exchanging posts with another applicant) without requiring some other applicant to be worse off. There are many Pareto-optimal matchings and so we need stronger definitions: a matching is rank-maximal [8] if it allocates the maximum number of applicants to their first choice, and then subject to this, the maximum number to their second choice, and so on. Such a matching has the lexicographically maximum tuple (n 1 , n 2 , .…”

Section: Introductionmentioning

confidence: 99%

Bounded Unpopularity Matchings

Huang

Kavitha

Michail

et al. 2008

Algorithm Theory – SWAT 2008

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Abstract. We investigate the following problem: given a set of jobs and a set of people with preferences over the jobs, what is the optimal way of matching people to jobs? Here we consider the notion of popularity. A matching M is popular if there is no matching M such that more people prefer M to M than the other way around. Determining whether a given instance admits a popular matching and, if so, finding one, was studied in [2]. If there is no popular matching, a reasonable substitute is a matching whose unpopularity is bounded. We consider two measures of unpopularity -unpopularity factor denoted by u(M) and unpopularity margin denoted by g(M). It has recently been shown that computing a matching M with the minimum value of u(M) or g(M) is NP-hard, and that if G does not admit a popular matching, then we have u(M) ≥ 2 for all matchings M in G.Here we show that a matching M that achieves u(M) = 2 can be computed in O(m √ n) time (where m is the number of edges in G and n is the number of nodes) provided a certain graph H admits a matching that matches all nodes in A. We also describe a sequence of graphs: H = H 2 , H 3 , . . . , H k such that if H k admits a matching that matches all nodes in A, then we can compute in O(km √ n) time a matching M such that u(M) ≤ k − 1 and g(M) ≤ n(1 − 2 k ). We ran our algorithm on random graphs and our simulation results suggest that our algorithm computes a matching with low unpopularity.

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“…The current fastest algorithm to compute a rank-maximal matching in the one-sided preference lists model takes time O(min{r * m √ n, mn, r * n ω }) [15], where r * is the largest rank used in a rank-maximal matching. In the one-sided preference lists setting, each edge has a unique rank associated with it, thus the edge set E is partitioned into E 1∪ E 2∪ · · ·∪ E r -this partition enables the problem of computing a rank-maximal matching to be reduced to computing r * maximum cardinality matchings in certain subgraphs of G. Our fair matching algorithm can be easily modified to compute a rank-maximal matching in the two-sided preference lists model.…”

Section: Introductionmentioning

confidence: 99%

Fair Matchings and Related Problems

et al. 2015

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Let G = (A ∪ B, E) be a bipartite graph, where every vertex ranks its neighbors in an order of preference (with ties allowed) and let r be the worst rank used. A matching M is fair in G if it has maximum cardinality, subject to this, M matches the minimum number of vertices to rank r neighbors, subject to that, M matches the minimum number of vertices to rank (r − 1) neighbors, and so on. We show an efficient combinatorial algorithm based on LP duality to compute a fair matching in G. We also show a scaling based algorithm for the fair b-matching problem.Our two algorithms can be extended to solve other profile-based matching problems. In designing our combinatorial algorithm, we show how to solve a generalized version of the minimum weighted vertex cover problem in bipartite graphs, using a single-source shortest paths computation-this can be of independent interest.

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Rank-maximal matchings

Cited by 97 publications

References 5 publications

Assigning Papers to Referees

Assigning Papers to Referees

Bounded Unpopularity Matchings

Fair Matchings and Related Problems

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