{"id":"https://openalex.org/W2618393581","doi":"https://doi.org/10.1007/s00453-020-00794-4","title":"Obtaining a Proportional Allocation by Deleting Items","display_name":"Obtaining a Proportional Allocation by Deleting Items","publication_year":2021,"publication_date":"2021-03-26","ids":{"openalex":"https://openalex.org/W2618393581","doi":"https://doi.org/10.1007/s00453-020-00794-4","mag":"2618393581","pmid":"https://pubmed.ncbi.nlm.nih.gov/34720294"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-020-00794-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-020-00794-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-020-00794-4.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-020-00794-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034565864","display_name":"Britta Dorn","orcid":null},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Britta Dorn","raw_affiliation_strings":["University of T\u00fcbingen, T\u00fcbingen, Germany"],"affiliations":[{"raw_affiliation_string":"University of T\u00fcbingen, T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068702258","display_name":"Ronald de Haan","orcid":"https://orcid.org/0000-0003-2023-0586"},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Ronald de Haan","raw_affiliation_strings":["ILLC, University of Amsterdam, Amsterdam, the Netherlands"],"affiliations":[{"raw_affiliation_string":"ILLC, University of Amsterdam, Amsterdam, the Netherlands","institution_ids":["https://openalex.org/I887064364"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070244460","display_name":"Ildik\u00f3 Schlotter","orcid":"https://orcid.org/0000-0002-0114-8280"},"institutions":[{"id":"https://openalex.org/I4210155320","display_name":"ELTE Centre for Economic and Regional Studies","ror":"https://ror.org/051ea1411","country_code":"HU","type":"facility","lineage":["https://openalex.org/I106118109","https://openalex.org/I4210155320"]},{"id":"https://openalex.org/I29770179","display_name":"Budapest University of Technology and Economics","ror":"https://ror.org/02w42ss30","country_code":"HU","type":"education","lineage":["https://openalex.org/I29770179"]},{"id":"https://openalex.org/I4210147073","display_name":"Institute of Economics","ror":"https://ror.org/05ng8e884","country_code":"HU","type":"facility","lineage":["https://openalex.org/I106118109","https://openalex.org/I4210147073","https://openalex.org/I4210155320"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Ildik\u00f3 Schlotter","raw_affiliation_strings":["Budapest University of Technology and Economics, and Centre for Economic and Regional Studies, Institute of Economics, Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"Budapest University of Technology and Economics, and Centre for Economic and Regional Studies, Institute of Economics, Budapest, Hungary","institution_ids":["https://openalex.org/I4210155320","https://openalex.org/I4210147073","https://openalex.org/I29770179"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070244460"],"corresponding_institution_ids":["https://openalex.org/I29770179","https://openalex.org/I4210147073","https://openalex.org/I4210155320"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.2955,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.72128636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"83","issue":"5","first_page":"1559","last_page":"1603"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5065850019454956},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.505122721195221},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4925316274166107},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48953017592430115},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.48720043897628784},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4643424451351166},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4047022759914398},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37642142176628113}],"concepts":[{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5065850019454956},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.505122721195221},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4925316274166107},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48953017592430115},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.48720043897628784},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4643424451351166},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4047022759914398},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37642142176628113},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s00453-020-00794-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-020-00794-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-020-00794-4.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmid:34720294","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34720294","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":null},{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/2603c6ae-a78e-4f9b-9d41-85e89d223994","is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/obtaining-a-proportional-allocation-by-deleting-items(2603c6ae-a78e-4f9b-9d41-85e89d223994).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Dorn, B, de Haan, R & Schlotter, I 2021, 'Obtaining a Proportional Allocation by Deleting Items', Algorithmica, vol. 83, no. 5, pp. 1559\u20131603. https://doi.org/10.1007/s00453-020-00794-4","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:dare.uva.nl:openaire/2603c6ae-a78e-4f9b-9d41-85e89d223994","is_oa":true,"landing_page_url":"https://hdl.handle.net/11245.1/2603c6ae-a78e-4f9b-9d41-85e89d223994","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dorn, B, de Haan, R & Schlotter, I 2021, 'Obtaining a Proportional Allocation by Deleting Items', Algorithmica, vol. 83, no. 5, pp. 1559\u20131603. https://doi.org/10.1007/s00453-020-00794-4","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:europepmc.org:7442629","is_oa":true,"landing_page_url":"http://europepmc.org/pmc/articles/PMC8550255","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8550255","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8550255","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithmica","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s00453-020-00794-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-020-00794-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-020-00794-4.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1533313245","display_name":null,"funder_award_id":"LP2016-3/2018","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G2656834856","display_name":null,"funder_award_id":"J4047","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G2845247602","display_name":null,"funder_award_id":"K128611","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G291076202","display_name":null,"funder_award_id":"K-124171","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G3711806682","display_name":null,"funder_award_id":"K124171","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G5289528719","display_name":null,"funder_award_id":"124171","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G5839530784","display_name":null,"funder_award_id":"K128611","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G6391809890","display_name":null,"funder_award_id":"Momentum","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G7764815442","display_name":null,"funder_award_id":"LP2016-3","funder_id":"https://openalex.org/F4320322192","funder_display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia"},{"id":"https://openalex.org/G8083627941","display_name":null,"funder_award_id":"K12417","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"}],"funders":[{"id":"https://openalex.org/F4320311358","display_name":"Budapesti M\u0171szaki \u00e9s Gazdas\u00e1gtudom\u00e1nyi Egyetem","ror":"https://ror.org/02w42ss30"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320321994","display_name":"Hungarian Scientific Research Fund","ror":"https://ror.org/00v349e63"},{"id":"https://openalex.org/F4320322192","display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia","ror":"https://ror.org/02ks8qq67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2618393581.pdf","grobid_xml":"https://content.openalex.org/works/W2618393581.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W987035227","https://openalex.org/W1494735819","https://openalex.org/W1527197079","https://openalex.org/W1570425181","https://openalex.org/W1942267539","https://openalex.org/W1995725694","https://openalex.org/W2007385106","https://openalex.org/W2022841964","https://openalex.org/W2044621860","https://openalex.org/W2107944092","https://openalex.org/W2116087731","https://openalex.org/W2121240598","https://openalex.org/W2130190334","https://openalex.org/W2157529519","https://openalex.org/W2161392628","https://openalex.org/W2246910425","https://openalex.org/W2343061998","https://openalex.org/W2499626972","https://openalex.org/W2575152399","https://openalex.org/W2788938373","https://openalex.org/W2913688336","https://openalex.org/W2949961730","https://openalex.org/W2950434194","https://openalex.org/W2962833396","https://openalex.org/W2972474670","https://openalex.org/W2997332295","https://openalex.org/W3121700742","https://openalex.org/W4292230561","https://openalex.org/W4298227433"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W2002282073","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W1991411408","https://openalex.org/W2383918176"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,29,38,43,50,85,93,104,117,130,144,163,178,198,236],"following":[3],"control":[4],"problem":[5,56,105,164],"on":[6,129],"fair":[7],"allocation":[8,48,170],"of":[9,16,21,37,45,87,96,132,139,162,177,189],"indivisible":[10],"goods.":[11],"Given":[12],"a":[13,19,34,46,66,137,150,160,186],"set":[14,20],"<i>I</i>":[15],"items":[17,39,190],"and":[18,126,141,180,220],"agents,":[22,213,219],"each":[23],"having":[24],"strict":[25],"linear":[26],"preferences":[27],"over":[28],"items,":[30],"we":[31,53,77,121,148,157,166,221],"ask":[32],"for":[33,72,146,154,211,217],"minimum":[35,187],"subset":[36],"whose":[40],"deletion":[41],"guarantees":[42],"existence":[44],"proportional":[47,196],"in":[49,173,197],"remaining":[51],"instance;":[52],"call":[54],"this":[55,200],"Proportionality":[57],"by":[58,235],"Item":[59],"Deletion":[60],"(PID).":[61],"Our":[62],"main":[63],"result":[64,153],"is":[65,81,89,100,106,183,195,225],"polynomial-time":[67,215],"algorithm":[68],"that":[69,79,103,192,223],"solves":[70],"PID":[71,80,133],"three":[73],"agents.":[74],"By":[75],"contrast,":[76],"prove":[78,149],"computationally":[82],"intractable":[83],"when":[84,134,233],"number":[86,94,188,237],"agents":[88],"unbounded,":[90],"even":[91],"if":[92],"<i>k</i>":[95,238],"item":[97],"deletions":[98],"allowed":[99],"small-we":[101],"show":[102,222],"<mml:math":[107,171,193,206,226],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>W</mml:mi>":[108,227],"<mml:mo>[</mml:mo>":[109,228],"<mml:mn>3</mml:mn>":[110],"<mml:mo>]</mml:mo></mml:mrow>":[111,230],"</mml:math>":[112,209,231],"-hard":[113,210,232],"with":[114],"respect":[115],"to":[116,184,204],"parameter":[118],"<i>k</i>.":[119,142],"Additionally,":[120],"provide":[122],"some":[123],"tight":[124],"lower":[125],"upper":[127],"bounds":[128],"complexity":[131],"regarded":[135],"as":[136,175],"function":[138],"|<i>I</i>|":[140],"Considering":[143],"possibilities":[145],"approximation,":[147],"strong":[151],"inapproximability":[152],"PID.":[155],"Finally,":[156],"also":[158],"study":[159],"variant":[161,201],"where":[165],"are":[167],"given":[168],"an":[169],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c0</mml:mi></mml:math>":[172,194],"advance":[174],"part":[176],"input,":[179],"our":[181],"aim":[182],"delete":[185],"such":[191],"remainder;":[199],"turns":[202],"out":[203],"be":[205],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>N</mml:mi>":[207],"<mml:mi>P</mml:mi></mml:mrow>":[208],"six":[212],"but":[214],"solvable":[216],"two":[218],"it":[224],"<mml:mn>2</mml:mn>":[229],"parameterized":[234],"of.":[239]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}