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Rank-maximal matchings

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Katarzyna E. PaluchAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 2, Issue 4

Pages 602 - 610

https://doi.org/10.1145/1198513.1198520

Published: 01 October 2006 Publication History

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Abstract

Suppose that each member of a set A of applicants ranks a subset of a set P of posts in an order of preference, possibly involving ties. A matching is a set of (applicant, post) pairs such that each applicant and each post appears in at most one pair. A rank-maximal matching is one in which the maximum possible number of applicants are matched to their first choice post, and subject to that condition, the maximum possible number are matched to their second choice post, and so on. This is a relevant concept in any practical matching situation and it was first studied by Irving [2003].We give an algorithm to compute a rank-maximal matching with running time O(min(n + C,C √n)m), where C is the maximal rank of an edge used in a rank-maximal matching, n is the number of applicants and posts and m is the total size of the preference lists.

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Cited By

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H.V. VNimbhorkar PDastani MSichman JAlechina NDignum V(2024)Weighted Proportional Allocations of Indivisible Goods and Chores: Insights via MatchingsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662931(780-788)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.5555/3635637.3662931
Tasnim MWeesie YGhebreab SBaak M(2024)Strategic manipulation of preferences in the rank minimization mechanismAutonomous Agents and Multi-Agent Systems10.1007/s10458-024-09676-338:2Online publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1007/s10458-024-09676-3
Faenza YStein CWan J(2024)Von Neumann-Morgenstern Stability and Internal Closedness in Matching TheoryInteger Programming and Combinatorial Optimization10.1007/978-3-031-59835-7_13(168-181)Online publication date: 3-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-59835-7_13
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Index Terms

Rank-maximal matchings
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms

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Rank-maximal matchings – structure and algorithms
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Let G = ( A ∪ P , E ) be a bipartite graph where A denotes a set of applicants, P denotes a set of posts and ranks on the edges denote preferences of the agents over posts. A matching M in G is rank-maximal if it matches the maximum ...
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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 2, Issue 4

October 2006

233 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1198513

Issue’s Table of Contents

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Publication History

Published: 01 October 2006

Published in TALG Volume 2, Issue 4

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H.V. VNimbhorkar PDastani MSichman JAlechina NDignum V(2024)Weighted Proportional Allocations of Indivisible Goods and Chores: Insights via MatchingsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662931(780-788)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.5555/3635637.3662931
Tasnim MWeesie YGhebreab SBaak M(2024)Strategic manipulation of preferences in the rank minimization mechanismAutonomous Agents and Multi-Agent Systems10.1007/s10458-024-09676-338:2Online publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1007/s10458-024-09676-3
Faenza YStein CWan J(2024)Von Neumann-Morgenstern Stability and Internal Closedness in Matching TheoryInteger Programming and Combinatorial Optimization10.1007/978-3-031-59835-7_13(168-181)Online publication date: 3-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-59835-7_13
Madathil JMisra NSethia AAgmon NAn BRicci AYeoh W(2023)The Complexity of Minimizing Envy in House AllocationProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3599039(2673-2675)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3599039
Hosseini HSikdar SVaish RXia LAgmon NAn BRicci AYeoh W(2023)Fairly Dividing Mixtures of Goods and Chores under Lexicographic PreferencesProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598632(152-160)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598632
Guo XSikdar SXia LCao YWang HElkind E(2023)First-choice maximality meets ex-ante and ex-post fairnessProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/303(2719-2727)Online publication date: 19-Aug-2023
https://dl.acm.org/doi/10.24963/ijcai.2023/303
Cheng Y(2023)Min-Max Optimal Matching2023 IEEE Integrated STEM Education Conference (ISEC)10.1109/ISEC57711.2023.10402347(309-316)Online publication date: 11-Mar-2023
https://doi.org/10.1109/ISEC57711.2023.10402347
Ghosal PKunysz APaluch K(2023)The dynamics of rank-maximal and popular matchingsTheoretical Computer Science10.1016/j.tcs.2023.114083972:COnline publication date: 13-Sep-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.114083
Aziz HHuang XMattei NSegal-Halevi E(2023)Computing welfare-Maximizing fair allocations of indivisible goodsEuropean Journal of Operational Research10.1016/j.ejor.2022.10.013307:2(773-784)Online publication date: Jun-2023
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Galichon AGhelfi OHenry M(2023)Stable and extremely unequalEconomics Letters10.1016/j.econlet.2023.111101226(111101)Online publication date: May-2023
https://doi.org/10.1016/j.econlet.2023.111101
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