{"id":"https://openalex.org/W2998253363","doi":"https://doi.org/10.1007/s10107-019-01460-6","title":"Stronger MIP formulations for the Steiner forest problem","display_name":"Stronger MIP formulations for the Steiner forest problem","publication_year":2020,"publication_date":"2020-01-03","ids":{"openalex":"https://openalex.org/W2998253363","doi":"https://doi.org/10.1007/s10107-019-01460-6","mag":"2998253363"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-019-01460-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-019-01460-6","pdf_url":null,"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://doi.org/10.1007/s10107-019-01460-6","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070779569","display_name":"Daniel R. Schmidt","orcid":"https://orcid.org/0000-0001-7381-912X"},"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":true,"raw_author_name":"Daniel Schmidt","raw_affiliation_strings":["Institute of Computer Science, University of Bonn, Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Bonn, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065818594","display_name":"Bernd Zey","orcid":"https://orcid.org/0000-0003-2551-9653"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bernd Zey","raw_affiliation_strings":["Department of Computer Science, Chair 11, TU Dortmund, Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Chair 11, TU Dortmund, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112617624","display_name":"Fran\u00e7ois Margot","orcid":null},"institutions":[{"id":"https://openalex.org/I4780363","display_name":"Pittsburg State University","ror":"https://ror.org/04hteea03","country_code":"US","type":"education","lineage":["https://openalex.org/I4780363"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fran\u00e7ois Margot","raw_affiliation_strings":["Pittsburg, USA"],"affiliations":[{"raw_affiliation_string":"Pittsburg, USA","institution_ids":["https://openalex.org/I4780363"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070779569"],"corresponding_institution_ids":["https://openalex.org/I135140700"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":0.2075,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.48785484,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"186","issue":"1-2","first_page":"373","last_page":"407"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9976999759674072,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9908999800682068,"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":0.9850000143051147,"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":0.8676302433013916},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.744932234287262},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.7199744582176208},{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.6886048316955566},{"id":"https://openalex.org/keywords/branch-and-cut","display_name":"Branch and cut","score":0.5320751667022705},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4931018054485321},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47497624158859253},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.45917701721191406},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4585456848144531},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4218662679195404},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36960190534591675},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10423263907432556}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8676302433013916},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.744932234287262},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.7199744582176208},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.6886048316955566},{"id":"https://openalex.org/C50797617","wikidata":"https://www.wikidata.org/wiki/Q498566","display_name":"Branch and cut","level":3,"score":0.5320751667022705},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4931018054485321},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47497624158859253},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.45917701721191406},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4585456848144531},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4218662679195404},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36960190534591675},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10423263907432556},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":1,"locations":[{"id":"doi:10.1007/s10107-019-01460-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-019-01460-6","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.1007/s10107-019-01460-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-019-01460-6","pdf_url":null,"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":"Life in Land","score":0.7200000286102295,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1974745840","https://openalex.org/W1976584101","https://openalex.org/W1994247939","https://openalex.org/W1999578543","https://openalex.org/W2001139415","https://openalex.org/W2004305790","https://openalex.org/W2006443810","https://openalex.org/W2011823863","https://openalex.org/W2022912747","https://openalex.org/W2027515293","https://openalex.org/W2041708730","https://openalex.org/W2043905543","https://openalex.org/W2048013200","https://openalex.org/W2064390891","https://openalex.org/W2090359754","https://openalex.org/W2107547393","https://openalex.org/W2108303241","https://openalex.org/W2111072608","https://openalex.org/W2119918317","https://openalex.org/W2120899253","https://openalex.org/W2147534455","https://openalex.org/W2152216760","https://openalex.org/W2155239253","https://openalex.org/W2164245156","https://openalex.org/W2172955861","https://openalex.org/W2189656425","https://openalex.org/W2408539216","https://openalex.org/W2488314452","https://openalex.org/W2570206580","https://openalex.org/W2886653775","https://openalex.org/W2963996640","https://openalex.org/W3020660928","https://openalex.org/W4247103873"],"related_works":["https://openalex.org/W2769220156","https://openalex.org/W3006617646","https://openalex.org/W2009796757","https://openalex.org/W4210880521","https://openalex.org/W2046300504","https://openalex.org/W2143061299","https://openalex.org/W2734758384","https://openalex.org/W2941986668","https://openalex.org/W3116484972","https://openalex.org/W4232431455"],"abstract_inverted_index":{"Abstract":[0],"The":[1,44],"Steiner":[2],"forest":[3,10],"problem":[4,31],"asks":[5],"for":[6,29],"a":[7,13],"minimum":[8],"weight":[9],"that":[11,100,116],"spans":[12],"given":[14],"number":[15],"of":[16,89,105],"terminal":[17],"sets.":[18],"We":[19,76],"propose":[20],"new":[21,107],"cut-":[22],"and":[23,57,64,71,81,115],"flow-based":[24],"integer":[25],"linear":[26,35,102],"programming":[27,36,103],"formulations":[28,108],"the":[30,39,65,86,101,106,117,125],"which":[32],"yield":[33],"stronger":[34],"bounds":[37,104],"than":[38],"two":[40],"previous":[41,126],"strongest":[42],"formulations:":[43],"directed":[45],"cut":[46],"formulation":[47,68],"(Balakrishnan":[48],"et":[49],"al.":[50],"in":[51,59],"Oper":[52],"Res":[53],"37(5):716\u2013740,":[54],"1989;":[55],"Chopra":[56],"Rao":[58],"Math":[60],"Prog":[61],"64(1):209\u2013229,":[62],"1994)":[63],"advanced":[66],"flow":[67],"by":[69],"Magnanti":[70],"Raghavan":[72],"(Networks":[73],"45:61\u201379,":[74],"2005).":[75],"further":[77],"introduce":[78],"strengthening":[79],"constraints":[80],"provide":[82],"an":[83,95],"example":[84],"where":[85],"integrality":[87],"gap":[88],"our":[90],"models":[91],"is":[92],"1.5.":[93],"In":[94],"experimental":[96],"evaluation,":[97],"we":[98],"show":[99],"are":[109],"indeed":[110],"strong":[111],"on":[112,124],"practical":[113],"instances":[114],"related":[118],"branch-and-cut":[119],"algorithm":[120],"outperforms":[121],"algorithms":[122],"based":[123],"formulations.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}