{"id":"https://openalex.org/W2025742807","doi":"https://doi.org/10.1002/net.3230120202","title":"Finding a minimum equivalent graph of a digraph","display_name":"Finding a minimum equivalent graph of a digraph","publication_year":1982,"publication_date":"1982-06-01","ids":{"openalex":"https://openalex.org/W2025742807","doi":"https://doi.org/10.1002/net.3230120202","mag":"2025742807"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230120202","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230120202","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5079979604","display_name":"Silvano Martello","orcid":"https://orcid.org/0000-0001-6515-1406"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Silvano Martello","raw_affiliation_strings":["Istituto di Automatica, University of Bologna, Bologna, Italy","Istituto di Automatica - University of Bologna, Bologna, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Istituto di Automatica, University of Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]},{"raw_affiliation_string":"Istituto di Automatica - University of Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084320669","display_name":"Paolo Toth","orcid":"https://orcid.org/0000-0001-6846-5814"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Paolo Toth","raw_affiliation_strings":["Istituto di Automatica, University of Bologna, Bologna, Italy","Istituto di Automatica - University of Bologna, Bologna, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Istituto di Automatica, University of Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]},{"raw_affiliation_string":"Istituto di Automatica - University of Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":0.5498,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.63689727,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"12","issue":"2","first_page":"89","last_page":"100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9993000030517578,"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":0.9993000030517578,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11106","display_name":"Data Management and Algorithms","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/digraph","display_name":"Digraph","score":0.970344603061676},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.8821457028388977},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5470200777053833},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5330148339271545},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5181468725204468},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5035597681999207},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4515789747238159},{"id":"https://openalex.org/keywords/branch-and-bound","display_name":"Branch and bound","score":0.44177156686782837},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4133090376853943},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38979828357696533}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.970344603061676},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.8821457028388977},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5470200777053833},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5330148339271545},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5181468725204468},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5035597681999207},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4515789747238159},{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.44177156686782837},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4133090376853943},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38979828357696533},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230120202","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230120202","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W398974528","https://openalex.org/W423069184","https://openalex.org/W1981358946","https://openalex.org/W1995246641","https://openalex.org/W2070992781","https://openalex.org/W2076447414","https://openalex.org/W2104734478","https://openalex.org/W2118382442","https://openalex.org/W2401610261"],"related_works":["https://openalex.org/W2136512912","https://openalex.org/W2127267268","https://openalex.org/W2038088825","https://openalex.org/W2067910792","https://openalex.org/W2034343496","https://openalex.org/W2389899617","https://openalex.org/W1931020284","https://openalex.org/W4319942994","https://openalex.org/W2024470714","https://openalex.org/W2182290077"],"abstract_inverted_index":{"Abstract":[0],"The":[1,21],"problem":[2],"considered":[3],"is":[4,30,33,44,60],"that":[5,35],"of":[6,11,24],"removing":[7],"the":[8,27],"maximum":[9],"number":[10],"edges":[12],"from":[13,26],"a":[14,48,53],"digraph":[15],"without":[16],"affecting":[17],"its":[18,58],"reachability":[19],"properties.":[20],"worst\u2010case":[22],"performance":[23],"algorithms":[25],"related":[28],"literature":[29],"analyzed;":[31],"it":[32],"found":[34],"Hsu's":[36],"method":[37],"contains":[38],"some":[39],"mistakes.":[40],"A":[41],"new":[42],"algorithm":[43],"presented,":[45],"based":[46],"on":[47,52],"reduction":[49],"procedure":[50],"and":[51,55,64],"branch":[54],"bound":[56],"search;":[57],"efficiency":[59],"studied":[61],"both":[62],"theoretically":[63],"through":[65],"computational":[66],"experiments.":[67]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
