{"id":"https://openalex.org/W1524291506","doi":"https://doi.org/10.1007/s000370050010","title":"An exponential lower bound on the size of algebraic decision trees for Max","display_name":"An exponential lower bound on the size of algebraic decision trees for Max","publication_year":1998,"publication_date":"1998-12-01","ids":{"openalex":"https://openalex.org/W1524291506","doi":"https://doi.org/10.1007/s000370050010","mag":"1524291506"},"language":"en","primary_location":{"id":"doi:10.1007/s000370050010","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s000370050010","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-03049461","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058530409","display_name":"D. Grigoriev","orcid":"https://orcid.org/0000-0002-3521-5402"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. Grigoriev","raw_affiliation_strings":["Dept. of Computer Science and Mathematics, Penn State University, University Park, USA, e-mail: dima@cse.psu.edu, , , , , , US","Dept. of Computer Science and Mathematics, Penn State University, University Park, USA, e-mail: dima@cse.psu.edu, US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science and Mathematics, Penn State University, University Park, USA, e-mail: dima@cse.psu.edu, , , , , , US","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Dept. of Computer Science and Mathematics, Penn State University, University Park, USA, e-mail: dima@cse.psu.edu, US","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108090276","display_name":"Marek Karpi\u0144ski","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Karpinski","raw_affiliation_strings":["Dept. of Computer Science, University of Bonn, D-53117 Bonn, e-mail: marek@cs.uni-bonn.de, , , , , , DE","Dept. of Computer Science, University of Bonn, D-53117 Bonn, e-mail: marek@cs.uni-bonn.de, DE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science, University of Bonn, D-53117 Bonn, e-mail: marek@cs.uni-bonn.de, , , , , , DE","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"Dept. of Computer Science, University of Bonn, D-53117 Bonn, e-mail: marek@cs.uni-bonn.de, DE","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076560802","display_name":"Andrew Chi-Chih Yao","orcid":"https://orcid.org/0000-0002-3648-5594"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A.C. Yao","raw_affiliation_strings":["Dept. of Computer Science, Princeton University, Princeton, New Jersey 08544, USA, e-mail: yao@cs.princeton.edu, , , , , , US","Dept. of Computer Science, Princeton University, Princeton, New Jersey 08544, USA, e-mail: yao@cs.princeton.edu, , US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science, Princeton University, Princeton, New Jersey 08544, USA, e-mail: yao@cs.princeton.edu, , , , , , US","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Dept. of Computer Science, Princeton University, Princeton, New Jersey 08544, USA, e-mail: yao@cs.princeton.edu, , US","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.9743,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.72202919,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"7","issue":"3","first_page":"193","last_page":"203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980000257492065,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980000257492065,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9973999857902527,"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":0.807181179523468},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7797330617904663},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7468963861465454},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6432294845581055},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5585463643074036},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5211679935455322},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.49860644340515137},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4953109323978424},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.4358443021774292},{"id":"https://openalex.org/keywords/decision-problem","display_name":"Decision problem","score":0.42138880491256714},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.41178131103515625},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08917561173439026}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.807181179523468},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7797330617904663},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7468963861465454},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6432294845581055},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5585463643074036},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5211679935455322},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.49860644340515137},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4953109323978424},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.4358443021774292},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.42138880491256714},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.41178131103515625},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08917561173439026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s000370050010","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s000370050010","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Complexity","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.36.6104","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.6104","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.univ-rennes1.fr/~dima/pub/max.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.50.9780","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.9780","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.cs.uni-bonn.de/~marek/publications/MAX.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.55.6962","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.55.6962","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.icsi.berkeley.edu/pub/techreports/1995/tr-95-066.ps.gz","raw_type":"text"},{"id":"pmh:oai:HAL:hal-03049461v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03049461","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"Computational Complexity, 1998","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03049461v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03049461","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"Computational Complexity, 1998","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6899999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1547370557","https://openalex.org/W1552137875","https://openalex.org/W1963956809","https://openalex.org/W2013568176","https://openalex.org/W2028627293","https://openalex.org/W2028920479","https://openalex.org/W2044850435","https://openalex.org/W2059499348","https://openalex.org/W2059985428","https://openalex.org/W2093331391","https://openalex.org/W2131730715","https://openalex.org/W2151407355","https://openalex.org/W2752853835"],"related_works":["https://openalex.org/W1634993130","https://openalex.org/W1602624896","https://openalex.org/W32300376","https://openalex.org/W1519862060","https://openalex.org/W1974979356","https://openalex.org/W2084061773","https://openalex.org/W2794917831","https://openalex.org/W2104564563","https://openalex.org/W2013108996","https://openalex.org/W3023224836"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
