{"id":"https://openalex.org/W2152366635","doi":"https://doi.org/10.1016/s0304-3975(02)00228-1","title":"The equation A\u2297x=B\u2297y over (max,+)","display_name":"The equation A\u2297x=B\u2297y over (max,+)","publication_year":2003,"publication_date":"2003-02-01","ids":{"openalex":"https://openalex.org/W2152366635","doi":"https://doi.org/10.1016/s0304-3975(02)00228-1","mag":"2152366635"},"language":"en","primary_location":{"id":"doi:10.1016/s0304-3975(02)00228-1","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0304-3975(02)00228-1","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014053395","display_name":"R. A. Cuninghame\u2010Green","orcid":null},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"R.A. Cuninghame-Green","raw_affiliation_strings":["School of Mathematics and Statistics, The University of Birmingham, Edgbaston, B15 2TT Birmingham, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, The University of Birmingham, Edgbaston, B15 2TT Birmingham, UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057034818","display_name":"Peter Butkovi\u010d","orcid":"https://orcid.org/0000-0003-3912-9250"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"P. Butkovic","raw_affiliation_strings":["School of Mathematics and Statistics, The University of Birmingham, Edgbaston, B15 2TT Birmingham, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, The University of Birmingham, Edgbaston, B15 2TT Birmingham, UK","institution_ids":["https://openalex.org/I79619799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057034818"],"corresponding_institution_ids":["https://openalex.org/I79619799"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":null,"fwci":1.4663,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.83112476,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"293","issue":"1","first_page":"3","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9958999752998352,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9958999752998352,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9889000058174133,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7502198219299316},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6142306327819824},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5786837339401245},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5716003179550171},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4901340901851654},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4659736156463623},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41259488463401794},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30084991455078125},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10005700588226318}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7502198219299316},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6142306327819824},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5786837339401245},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5716003179550171},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4901340901851654},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4659736156463623},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41259488463401794},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30084991455078125},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10005700588226318},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0304-3975(02)00228-1","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0304-3975(02)00228-1","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/0b22a399-f9bf-43e7-81f5-1e3b4f2df0d0","is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/0b22a399-f9bf-43e7-81f5-1e3b4f2df0d0","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cuninghame-Green, R & Butkovic, P 2003, 'The equation Ax=By over (max, +)', Theoretical Computer Science, vol. 293, no. 1, pp. 3-12. https://doi.org/10.1016/S0304-3975(02)00228-1","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W25288802","https://openalex.org/W802370431","https://openalex.org/W1557235141","https://openalex.org/W1991466857","https://openalex.org/W4213373825","https://openalex.org/W4250661196","https://openalex.org/W6622943767"],"related_works":["https://openalex.org/W1598955744","https://openalex.org/W2055836843","https://openalex.org/W2755775996","https://openalex.org/W4384111961","https://openalex.org/W2951710344","https://openalex.org/W2773728674","https://openalex.org/W2144602163","https://openalex.org/W2204136089","https://openalex.org/W3131818128","https://openalex.org/W2142539551"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":5}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
