{"id":"https://openalex.org/W3033463406","doi":"https://doi.org/10.1002/net.22031","title":"An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs","display_name":"An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs","publication_year":2021,"publication_date":"2021-02-28","ids":{"openalex":"https://openalex.org/W3033463406","doi":"https://doi.org/10.1002/net.22031","mag":"3033463406"},"language":"en","primary_location":{"id":"doi:10.1002/net.22031","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.22031","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2006.02988","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057202379","display_name":"Logan A. Smith","orcid":"https://orcid.org/0000-0002-6919-8217"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Logan A. Smith","raw_affiliation_strings":["Department of Computational and Applied Mathematics Rice University  Houston 77005 Texas USA","Department of Computational and Applied Mathematics Rice University Houston 77005 Texas USA"],"raw_orcid":"https://orcid.org/0000-0002-6919-8217","affiliations":[{"raw_affiliation_string":"Department of Computational and Applied Mathematics Rice University  Houston 77005 Texas USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Computational and Applied Mathematics Rice University Houston 77005 Texas USA","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032445968","display_name":"David Mildebrath","orcid":null},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Mildebrath","raw_affiliation_strings":["Department of Computational and Applied Mathematics Rice University  Houston 77005 Texas USA","Department of Computational and Applied Mathematics Rice University Houston 77005 Texas USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational and Applied Mathematics Rice University  Houston 77005 Texas USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Computational and Applied Mathematics Rice University Houston 77005 Texas USA","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025235914","display_name":"Illya V. Hicks","orcid":"https://orcid.org/0000-0002-7815-796X"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Illya V. Hicks","raw_affiliation_strings":["Department of Computational and Applied Mathematics Rice University  Houston 77005 Texas USA","Department of Computational and Applied Mathematics Rice University Houston 77005 Texas USA"],"raw_orcid":"https://orcid.org/0000-0002-7815-796X","affiliations":[{"raw_affiliation_string":"Department of Computational and Applied Mathematics Rice University  Houston 77005 Texas USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Computational and Applied Mathematics Rice University Houston 77005 Texas USA","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057202379"],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02266492,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"79","issue":"1","first_page":"3","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9976999759674072,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.6894459128379822},{"id":"https://openalex.org/keywords/rainbow","display_name":"Rainbow","score":0.6526440382003784},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.6493712663650513},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.6473670601844788},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5738029479980469},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5478649735450745},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5417609214782715},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5101397633552551},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4982571601867676},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4231397807598114},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35906079411506653},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35447168350219727},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34498825669288635},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.265438050031662},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06448885798454285}],"concepts":[{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.6894459128379822},{"id":"https://openalex.org/C2776558979","wikidata":"https://www.wikidata.org/wiki/Q1052","display_name":"Rainbow","level":2,"score":0.6526440382003784},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6493712663650513},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.6473670601844788},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5738029479980469},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5478649735450745},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5417609214782715},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5101397633552551},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4982571601867676},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4231397807598114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35906079411506653},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35447168350219727},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34498825669288635},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.265438050031662},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06448885798454285},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1002/net.22031","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.22031","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"},{"id":"pmh:oai:arXiv.org:2006.02988","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.02988","pdf_url":"https://arxiv.org/pdf/2006.02988","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3033463406","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2006.02988.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2006.02988","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2006.02988","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2006.02988","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.02988","pdf_url":"https://arxiv.org/pdf/2006.02988","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2961051826","display_name":"Collaborative Research:   Zero Forcing on Graphs: Computation and Applications","funder_award_id":"1720225","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306078","display_name":"U.S. Department of Defense","ror":"https://ror.org/0447fe631"},{"id":"https://openalex.org/F4320310133","display_name":"Rice University","ror":"https://ror.org/008zs3103"},{"id":"https://openalex.org/F4320333566","display_name":"National Defense Science and Engineering Graduate","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3033463406.pdf","grobid_xml":"https://content.openalex.org/works/W3033463406.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W131619556","https://openalex.org/W133641357","https://openalex.org/W1484040084","https://openalex.org/W1556758605","https://openalex.org/W1592788572","https://openalex.org/W1676827047","https://openalex.org/W1749394499","https://openalex.org/W1767950408","https://openalex.org/W1967140769","https://openalex.org/W1968143987","https://openalex.org/W1970686950","https://openalex.org/W1972760347","https://openalex.org/W1980661021","https://openalex.org/W1990357129","https://openalex.org/W2001341021","https://openalex.org/W2005708967","https://openalex.org/W2006934540","https://openalex.org/W2013307517","https://openalex.org/W2015953751","https://openalex.org/W2024838210","https://openalex.org/W2032081889","https://openalex.org/W2034743574","https://openalex.org/W2047875736","https://openalex.org/W2049716158","https://openalex.org/W2094234423","https://openalex.org/W2094836579","https://openalex.org/W2112090702","https://openalex.org/W2131169256","https://openalex.org/W2132022337","https://openalex.org/W2150438015","https://openalex.org/W2155956600","https://openalex.org/W2201553700","https://openalex.org/W2294347342","https://openalex.org/W2312958607","https://openalex.org/W2544075308","https://openalex.org/W2589833411","https://openalex.org/W2594540369","https://openalex.org/W2599097688","https://openalex.org/W2920565532","https://openalex.org/W2950884311","https://openalex.org/W2962833099","https://openalex.org/W3100069540","https://openalex.org/W3101413764","https://openalex.org/W3143219376","https://openalex.org/W4233791220","https://openalex.org/W4248704047"],"related_works":["https://openalex.org/W3133944896","https://openalex.org/W2762756801","https://openalex.org/W2793504318","https://openalex.org/W2157507931","https://openalex.org/W3163817225","https://openalex.org/W3036315659","https://openalex.org/W2137560467","https://openalex.org/W2774158340","https://openalex.org/W2795065148","https://openalex.org/W606113","https://openalex.org/W2794875535","https://openalex.org/W3080569475","https://openalex.org/W2084471831","https://openalex.org/W2808696501","https://openalex.org/W2095525633","https://openalex.org/W2767162673","https://openalex.org/W3002493401","https://openalex.org/W1570588782","https://openalex.org/W2522826197","https://openalex.org/W2090339428"],"abstract_inverted_index":{"Abstract":[0],"We":[1,24,60,105],"present":[2,43],"an":[3,69],"integer":[4,63],"programming":[5],"model":[6],"to":[7,28,84,123],"compute":[8],"the":[9,29,62,78,95,100,107,114],"strong":[10,101,115],"rainbow":[11,102,116],"connection":[12,103,117],"number,":[13],"src":[14,49],"(":[15,50],"G":[16,22,51],"),":[17],"of":[18,56,80,109,119],"any":[19],"simple":[20],"graph":[21],".":[23],"introduce":[25],"several":[26],"enhancements":[27],"proposed":[30],"model,":[31],"including":[32],"a":[33,37,44],"fast":[34],"heuristic,":[35],"and":[36,67],"variable":[38],"elimination":[39],"scheme.":[40],"Moreover,":[41],"we":[42,82],"novel":[45],"lower":[46,75],"bound":[47,76],"for":[48,99],")":[52],"which":[53,81],"may":[54],"be":[55,85],"independent":[57],"research":[58],"interest.":[59],"solve":[61],"program":[64],"both":[65],"directly":[66],"using":[68],"alternative":[70],"method":[71],"based":[72],"on":[73],"iterative":[74],"improvement,":[77],"latter":[79],"show":[83],"highly":[86],"effective":[87],"in":[88],"practice.":[89],"To":[90],"our":[91,110],"knowledge,":[92],"these":[93],"are":[94],"first":[96],"computational":[97],"methods":[98,111],"problem.":[104],"demonstrate":[106],"efficacy":[108],"by":[112],"computing":[113],"numbers":[118],"graphs":[120],"containing":[121],"up":[122],"379":[124],"vertices.":[125]},"counts_by_year":[],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
