{"id":"https://openalex.org/W2985441210","doi":"https://doi.org/10.1007/s10107-022-01848-x","title":"An exponential lower bound for Zadeh\u2019s pivot rule","display_name":"An exponential lower bound for Zadeh\u2019s pivot rule","publication_year":2022,"publication_date":"2022-07-19","ids":{"openalex":"https://openalex.org/W2985441210","doi":"https://doi.org/10.1007/s10107-022-01848-x","mag":"2985441210"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-022-01848-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-022-01848-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-022-01848-x.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-022-01848-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021248592","display_name":"Yann Disser","orcid":"https://orcid.org/0000-0002-2085-0454"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Yann Disser","raw_affiliation_strings":["Department of Mathematics, TU Darmstadt, Darmstadt, Germany"],"raw_orcid":"https://orcid.org/0000-0002-2085-0454","affiliations":[{"raw_affiliation_string":"Department of Mathematics, TU Darmstadt, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044839312","display_name":"Oliver Friedmann","orcid":null},"institutions":[{"id":"https://openalex.org/I3018771216","display_name":"LMU Klinikum","ror":"https://ror.org/02jet3w32","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I3018771216","https://openalex.org/I8204097"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Oliver Friedmann","raw_affiliation_strings":["Department of Informatics, LMU Munich, Mnchen, Germany","Department of Informatics, LMU Munich, M\u00fcnchen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, LMU Munich, Mnchen, Germany","institution_ids":["https://openalex.org/I3018771216","https://openalex.org/I8204097"]},{"raw_affiliation_string":"Department of Informatics, LMU Munich, M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I3018771216","https://openalex.org/I8204097"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068029953","display_name":"Alexander V. Hopp","orcid":"https://orcid.org/0000-0003-1729-1046"},"institutions":[{"id":"https://openalex.org/I164928964","display_name":"Merck (Germany)","ror":"https://ror.org/04b2dty93","country_code":"DE","type":"company","lineage":["https://openalex.org/I164928964"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alexander V. Hopp","raw_affiliation_strings":["Merck KGaA, Darmstadt, Germany"],"raw_orcid":"https://orcid.org/0000-0003-1729-1046","affiliations":[{"raw_affiliation_string":"Merck KGaA, Darmstadt, Germany","institution_ids":["https://openalex.org/I164928964"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021248592"],"corresponding_institution_ids":["https://openalex.org/I31512782"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":1.6593,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.85081627,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"199","issue":"1-2","first_page":"865","last_page":"936"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9991999864578247,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9972000122070312,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.989300012588501,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7703777551651001},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6107913255691528},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4855477511882782},{"id":"https://openalex.org/keywords/simplex-algorithm","display_name":"Simplex algorithm","score":0.4738866686820984},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4109905958175659},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3330789804458618},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32251641154289246},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.23159575462341309}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7703777551651001},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6107913255691528},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4855477511882782},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.4738866686820984},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4109905958175659},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3330789804458618},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32251641154289246},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.23159575462341309},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-022-01848-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-022-01848-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-022-01848-x.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:153069","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/view/person/Disser=3AYann=3A=3A.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"}],"best_oa_location":{"id":"doi:10.1007/s10107-022-01848-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-022-01848-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-022-01848-x.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7599999904632568}],"awards":[{"id":"https://openalex.org/G2030772380","display_name":null,"funder_award_id":"GSC 233/2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323384","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2985441210.pdf","grobid_xml":"https://content.openalex.org/works/W2985441210.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W186942940","https://openalex.org/W968309248","https://openalex.org/W1503025934","https://openalex.org/W1514240489","https://openalex.org/W1862519416","https://openalex.org/W1928484725","https://openalex.org/W1981423455","https://openalex.org/W2022121413","https://openalex.org/W2023067115","https://openalex.org/W2033040247","https://openalex.org/W2040483032","https://openalex.org/W2044413922","https://openalex.org/W2061874298","https://openalex.org/W2069730673","https://openalex.org/W2073264848","https://openalex.org/W2076680677","https://openalex.org/W2079737176","https://openalex.org/W2080654168","https://openalex.org/W2106318612","https://openalex.org/W2109237987","https://openalex.org/W2127470768","https://openalex.org/W2139819161","https://openalex.org/W2141252092","https://openalex.org/W2151888904","https://openalex.org/W2152479402","https://openalex.org/W2494547223","https://openalex.org/W2502103274","https://openalex.org/W2778541828","https://openalex.org/W3105031228","https://openalex.org/W4235914513","https://openalex.org/W4298023569","https://openalex.org/W6805787914"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2038812594","https://openalex.org/W2359118052","https://openalex.org/W4386195899","https://openalex.org/W2031152868","https://openalex.org/W2809374263","https://openalex.org/W2592261830","https://openalex.org/W2982347821","https://openalex.org/W2374829073","https://openalex.org/W2083193613"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"question":[2],"whether":[3],"the":[4,15,36,54,59,84,96,104],"Simplex":[5],"Algorithm":[6,99,107],"admits":[7],"an":[8],"efficient":[9],"pivot":[10,27,62],"rule":[11,38,52,63,78,121],"remains":[12],"one":[13],"of":[14],"most":[16,55],"important":[17],"open":[18],"questions":[19],"in":[20,80,83,122],"discrete":[21],"optimization.":[22],"While":[23],"many":[24],"natural,":[25],"deterministic":[26,61],"rules":[28],"are":[29],"known":[30],"to":[31,41,95],"yield":[32],"exponential":[33,82,116],"running":[34,45,66],"times,":[35],"random-facet":[37],"was":[39],"shown":[40],"have":[42],"a":[43,48,70,92],"subexponential":[44,65],"time.":[46,67],"For":[47],"long":[49],"time,":[50],"Zadeh\u2019s":[51,77,120],"remained":[53],"prominent":[56],"candidate":[57],"for":[58,100,108,119],"first":[60],"with":[64],"We":[68],"present":[69],"lower":[71,117],"bound":[72],"construction":[73,88],"that":[74,76],"shows":[75],"is":[79,89],"fact":[81],"worst":[85],"case.":[86],"Our":[87],"based":[90],"on":[91],"close":[93],"relation":[94],"Strategy":[97],"Improvement":[98],"Parity":[101],"Games":[102],"and":[103,112],"Policy":[105],"Iteration":[106],"Markov":[109],"Decision":[110],"Processes,":[111],"we":[113],"also":[114],"obtain":[115],"bounds":[118],"these":[123],"contexts.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}