Optimal Impartial Correspondences
We study mechanisms that select a subset of the vertex set of a directed graph in order to maximize the minimum indegree of any selected vertex, subject to an impartiality constraint that the selection of a particular vertex is independent of the outgoing edges of that vertex. For graphs with maximu...
Uloženo v:
| Vydáno v: | arXiv.org |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Paper |
| Jazyk: | angličtina |
| Vydáno: |
Ithaca
Cornell University Library, arXiv.org
11.01.2023
|
| Témata: | |
| ISSN: | 2331-8422 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | We study mechanisms that select a subset of the vertex set of a directed graph in order to maximize the minimum indegree of any selected vertex, subject to an impartiality constraint that the selection of a particular vertex is independent of the outgoing edges of that vertex. For graphs with maximum outdegree \(d\), we give a mechanism that selects at most \(d+1\) vertices and only selects vertices whose indegree is at least the maximum indegree in the graph minus one. We then show that this is best possible in the sense that no impartial mechanism can only select vertices with maximum degree, even without any restriction on the number of selected vertices. We finally obtain the following trade-off between the maximum number of vertices selected and the minimum indegree of any selected vertex: when selecting at most~\(k\) vertices out of \(n\), it is possible to only select vertices whose indegree is at least the maximum indegree minus \(\lfloor(n-2)/(k-1)\rfloor+1\). |
|---|---|
| AbstractList | We study mechanisms that select a subset of the vertex set of a directed graph in order to maximize the minimum indegree of any selected vertex, subject to an impartiality constraint that the selection of a particular vertex is independent of the outgoing edges of that vertex. For graphs with maximum outdegree \(d\), we give a mechanism that selects at most \(d+1\) vertices and only selects vertices whose indegree is at least the maximum indegree in the graph minus one. We then show that this is best possible in the sense that no impartial mechanism can only select vertices with maximum degree, even without any restriction on the number of selected vertices. We finally obtain the following trade-off between the maximum number of vertices selected and the minimum indegree of any selected vertex: when selecting at most~\(k\) vertices out of \(n\), it is possible to only select vertices whose indegree is at least the maximum indegree minus \(\lfloor(n-2)/(k-1)\rfloor+1\). |
| Author | Cembrano, Javier Klimm, Max Fischer, Felix |
| Author_xml | – sequence: 1 givenname: Javier surname: Cembrano fullname: Cembrano, Javier – sequence: 2 givenname: Felix surname: Fischer fullname: Fischer, Felix – sequence: 3 givenname: Max surname: Klimm fullname: Klimm, Max |
| BookMark | eNotjc1KAzEURoMoWGsfwJ3iesbk3iR3spTBn0Khm-5LmrmBKe1kTKbi4zugm_Od1XfuxPWQBhbiQclaN8bIF59_-u8aUKpaaqP1lVgAoqoaDXArVqUcpZRgCYzBhXjajlN_9qfH9Xn0eepna1POXMY0dDwELvfiJvpT4dX_LsXu_W3Xflab7ce6fd1U3gBVAaOXB2fcTMWdsnFWOHiwOhBjUD5Gh9YSR2M1k-vIhqhU9ORQxwaX4vnvdszp68Jl2h_TJQ9zcQ9kNTXSEOEvW8NByA |
| ContentType | Paper |
| Copyright | 2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: 2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | 8FE 8FG ABJCF ABUWG AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| DOI | 10.48550/arxiv.2301.04544 |
| DatabaseName | ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central Technology collection ProQuest One Community College ProQuest Central ProQuest SciTech Premium Collection ProQuest Engineering Collection Engineering Database ProQuest Central Premium ProQuest One Academic Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection |
| DatabaseTitle | Publicly Available Content Database Engineering Database Technology Collection ProQuest One Academic Middle East (New) ProQuest Central Essentials ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) Engineering Collection |
| DatabaseTitleList | Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: PIMPY name: Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 2331-8422 |
| Genre | Working Paper/Pre-Print |
| GroupedDBID | 8FE 8FG ABJCF ABUWG AFKRA ALMA_UNASSIGNED_HOLDINGS AZQEC BENPR BGLVJ CCPQU DWQXO FRJ HCIFZ L6V M7S M~E PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| ID | FETCH-LOGICAL-a527-c3fa0b959a0b1ed16f59a2ba264c7e3c1aff93667ef564e79d76cf11fa7934f83 |
| IEDL.DBID | BENPR |
| IngestDate | Mon Jun 30 09:20:37 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a527-c3fa0b959a0b1ed16f59a2ba264c7e3c1aff93667ef564e79d76cf11fa7934f83 |
| Notes | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| OpenAccessLink | https://www.proquest.com/docview/2764780577?pq-origsite=%requestingapplication% |
| PQID | 2764780577 |
| PQPubID | 2050157 |
| ParticipantIDs | proquest_journals_2764780577 |
| PublicationCentury | 2000 |
| PublicationDate | 20230111 |
| PublicationDateYYYYMMDD | 2023-01-11 |
| PublicationDate_xml | – month: 01 year: 2023 text: 20230111 day: 11 |
| PublicationDecade | 2020 |
| PublicationPlace | Ithaca |
| PublicationPlace_xml | – name: Ithaca |
| PublicationTitle | arXiv.org |
| PublicationYear | 2023 |
| Publisher | Cornell University Library, arXiv.org |
| Publisher_xml | – name: Cornell University Library, arXiv.org |
| SSID | ssj0002672553 |
| Score | 1.8188242 |
| SecondaryResourceType | preprint |
| Snippet | We study mechanisms that select a subset of the vertex set of a directed graph in order to maximize the minimum indegree of any selected vertex, subject to an... |
| SourceID | proquest |
| SourceType | Aggregation Database |
| SubjectTerms | Apexes Graph theory Vertex sets |
| Title | Optimal Impartial Correspondences |
| URI | https://www.proquest.com/docview/2764780577 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NSwMxEB20VfDkN37UUsFrbLObTTYnwdJiD9ZFe6inMskmUGi3dbcWf77JutWD4MVLSMglQzIvw-RlHsBNKoxMlaTEdLgmjKqIINUBQRXFKUfuIiVdik2I4TAej2VSJdyKila5wcQSqNOF9jnydiD8r0gXXYi75RvxqlH-dbWS0NiGuq9UxmpQv-8Nk-fvLEvAhYuZw6_nzLJ4Vxvzj-na85_prS8_x36BcHmz9Pf_u6YDqCe4NPkhbJnsCHZLRqcujuH6yYHBHGetgSeZOz-etbqlEsdykZU6osUJjPq9UfeBVHoIBKNAEB1a7CgZSddSk1JuXTdQ6EIaLUyoKVorQ86FsRFnRshUcG0pteh8kNk4PIVatsjMGbSQaWW16FATW2Y0IgplhIgd1imlLDuHxsbgSXWmi8mPtRd_T1_Cnhdl94kKShtQW-Xv5gp29Ho1LfJmtUVNz7J8caNk8Ji8fgLGGqCy |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3LTgIxFL1R0OjKd3ygjokuK3Qe7czCuEAJBEQSWbCbtJ02IcEBZxD1o_xH28LowsQdCzdNkyZNc3t7ent72gNwmVAZJTzCSNaIQD7mAWJYuIjxIEwIIzpSElZsgna74WAQ9Vbgs3gLY2iVBSZaoE7GwuTIqy41ryJ1dEFvJy_IqEaZ29VCQmPuFm358aaPbPlN607P75XrNu779SZaqAogFrgUCU-xGo-CSJdYJpgoXXU504GBoNITmCkVeYRQqQLiSxollAiFsWLak30VerrbVSj7BvwtU_DpO6XjEqoDdG9-d2p_Cquy7H04M2RrfG3-uvN_Ib7dxhpb_8wA21DusYnMdmBFpruwbtmqIt-Di0cNdM9s5LQMgV5j1MipW5WRyTi1Gqn5PvSXMagDKKXjVB6Cw3zBlaA1LEPlS8EYo1xSGmoc55wr_wgqhX3jxXrN4x_jHv_dfA4bzf5DJ-60uu0T2DTi8yYhg3EFStPsVZ7CmphNh3l2Zn3DgXjJU_EF_DH55Q |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Optimal+Impartial+Correspondences&rft.jtitle=arXiv.org&rft.au=Cembrano%2C+Javier&rft.au=Fischer%2C+Felix&rft.au=Klimm%2C+Max&rft.date=2023-01-11&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.2301.04544 |