Competitive Query Minimization for Stable Matching with One-Sided Uncertainty
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916323033874432 |
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| author | Bampis, Evripidis Dogeas, Konstantinos Erlebach, Thomas Megow, Nicole Schlöter, Jens Trehan, Amitabh |
| author_facet | Bampis, Evripidis Dogeas, Konstantinos Erlebach, Thomas Megow, Nicole Schlöter, Jens Trehan, Amitabh |
| contents | We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are unknown. An algorithm can make queries to reveal information about the preferences of the agents in B. We examine three query models: comparison queries, interviews, and set queries. Using competitive analysis, our aim is to design algorithms that minimize the number of queries required to solve the problem of finding a stable matching or verifying that a given matching is stable (or stable and optimal for the agents of one side). We present various upper and lower bounds on the best possible competitive ratio as well as results regarding the complexity of the offline problem of determining the optimal query set given full information. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10170 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Competitive Query Minimization for Stable Matching with One-Sided Uncertainty Bampis, Evripidis Dogeas, Konstantinos Erlebach, Thomas Megow, Nicole Schlöter, Jens Trehan, Amitabh Data Structures and Algorithms 68Q25 F.2.2; G.2.2 We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are unknown. An algorithm can make queries to reveal information about the preferences of the agents in B. We examine three query models: comparison queries, interviews, and set queries. Using competitive analysis, our aim is to design algorithms that minimize the number of queries required to solve the problem of finding a stable matching or verifying that a given matching is stable (or stable and optimal for the agents of one side). We present various upper and lower bounds on the best possible competitive ratio as well as results regarding the complexity of the offline problem of determining the optimal query set given full information. |
| title | Competitive Query Minimization for Stable Matching with One-Sided Uncertainty |
| topic | Data Structures and Algorithms 68Q25 F.2.2; G.2.2 |
| url | https://arxiv.org/abs/2407.10170 |