{"id":"https://openalex.org/W4396761170","doi":"https://doi.org/10.1007/s10107-024-02086-z","title":"A linear time algorithm for linearizing quadratic and higher-order shortest path problems","display_name":"A linear time algorithm for linearizing quadratic and higher-order shortest path problems","publication_year":2024,"publication_date":"2024-05-09","ids":{"openalex":"https://openalex.org/W4396761170","doi":"https://doi.org/10.1007/s10107-024-02086-z","pmid":"https://pubmed.ncbi.nlm.nih.gov/40026607"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-024-02086-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-024-02086-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-024-02086-z.pdf","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","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-024-02086-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056529887","display_name":"Eranda \u00c7ela","orcid":"https://orcid.org/0000-0002-5099-8804"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Eranda \u00c7ela","raw_affiliation_strings":["Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria"],"raw_orcid":"https://orcid.org/0000-0002-5099-8804","affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025216576","display_name":"Bettina Klinz","orcid":"https://orcid.org/0000-0002-6156-688X"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Bettina Klinz","raw_affiliation_strings":["Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria"],"raw_orcid":"https://orcid.org/0000-0002-6156-688X","affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065168862","display_name":"Stefan Lendl","orcid":"https://orcid.org/0000-0002-5660-5397"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Stefan Lendl","raw_affiliation_strings":["Institut of Operations and Information Systems, University of Graz, Graz, Austria"],"raw_orcid":"https://orcid.org/0000-0002-5660-5397","affiliations":[{"raw_affiliation_string":"Institut of Operations and Information Systems, University of Graz, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080746477","display_name":"Gerhard J. Woeginger","orcid":"https://orcid.org/0000-0001-8816-2693"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerhard J. Woeginger","raw_affiliation_strings":["Department of Computer Science, RWTH Aachen, Aachen, Germany"],"raw_orcid":"https://orcid.org/0000-0001-8816-2693","affiliations":[{"raw_affiliation_string":"Department of Computer Science, RWTH Aachen, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062230321","display_name":"Lasse Wulf","orcid":"https://orcid.org/0000-0001-7139-4092"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Lasse Wulf","raw_affiliation_strings":["Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria"],"raw_orcid":"https://orcid.org/0000-0001-7139-4092","affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062230321"],"corresponding_institution_ids":["https://openalex.org/I4092182"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.431,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62985096,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"210","issue":"1-2","first_page":"165","last_page":"188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.9891999959945679,"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"}},"topics":[{"id":"https://openalex.org/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.9891999959945679,"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"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9886000156402588,"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"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.986299991607666,"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/mathematics","display_name":"Mathematics","score":0.7693018913269043},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.7364187240600586},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.7305492162704468},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.5836972594261169},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5177925825119019},{"id":"https://openalex.org/keywords/k-shortest-path-routing","display_name":"K shortest path routing","score":0.4796743392944336},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.47113746404647827},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46690255403518677},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40373581647872925},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3501507341861725},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16028684377670288},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13955757021903992},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.07138267159461975}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7693018913269043},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.7364187240600586},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.7305492162704468},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.5836972594261169},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5177925825119019},{"id":"https://openalex.org/C70266271","wikidata":"https://www.wikidata.org/wiki/Q6343044","display_name":"K shortest path routing","level":4,"score":0.4796743392944336},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.47113746404647827},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46690255403518677},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40373581647872925},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3501507341861725},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16028684377670288},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13955757021903992},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.07138267159461975},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10107-024-02086-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-024-02086-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-024-02086-z.pdf","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"},{"id":"pmid:40026607","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40026607","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical programming","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:11870919","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11870919","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11870919/pdf/10107_2024_Article_2086.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Math Program","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s10107-024-02086-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-024-02086-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-024-02086-z.pdf","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":[],"awards":[{"id":"https://openalex.org/G6196800289","display_name":"Discrete Mathematics","funder_award_id":"W 1230","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G751256963","display_name":null,"funder_award_id":"FWF: W1230","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320310430","display_name":"TU Graz, Internationale Beziehungen und Mobilit\u00e4tsprogramme","ror":"https://ror.org/00d7xrm67"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4396761170.pdf"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W27436463","https://openalex.org/W607230564","https://openalex.org/W1168951679","https://openalex.org/W1964265873","https://openalex.org/W1964357023","https://openalex.org/W1980190773","https://openalex.org/W1985792422","https://openalex.org/W2033564834","https://openalex.org/W2049345634","https://openalex.org/W2087490340","https://openalex.org/W2120803586","https://openalex.org/W2138244558","https://openalex.org/W2554728250","https://openalex.org/W2602684069","https://openalex.org/W2964131403","https://openalex.org/W3007817717","https://openalex.org/W3200034092","https://openalex.org/W3200189330","https://openalex.org/W4377200014","https://openalex.org/W4377200044","https://openalex.org/W4388850884"],"related_works":["https://openalex.org/W4286247391","https://openalex.org/W2198982833","https://openalex.org/W2767202586","https://openalex.org/W4293054712","https://openalex.org/W2375775343","https://openalex.org/W2388654557","https://openalex.org/W2360981904","https://openalex.org/W2365712669","https://openalex.org/W2161960576","https://openalex.org/W1990043277"],"abstract_inverted_index":{"An":[0],"instance":[1,19,44,52],"of":[2,20,91],"the":[3,21,28,36,49,54,65,75,89,92,108],"NP-hard":[4],"Quadratic":[5],"Shortest":[6,23],"Path":[7,24],"Problem":[8,25],"(QSPP)":[9],"is":[10,15,45,81],"called":[11],"linearizable":[12,46],"iff":[13],"it":[14],"equivalent":[16],"to":[17,107],"an":[18],"classic":[22],"(SPP)":[26],"on":[27,67,83],"same":[29],"input":[30],"digraph.":[31],"The":[32,79],"linearization":[33],"problem":[34],"for":[35,64,94],"QSPP":[37,43,93],"(LinQSPP)":[38],"decides":[39],"whether":[40],"a":[41,59,84,101],"given":[42],"and":[47],"determines":[48],"corresponding":[50],"SPP":[51],"in":[53],"positive":[55],"case.":[56],"We":[57],"provide":[58],"novel":[60],"linear":[61],"time":[62],"algorithm":[63,80],"LinQSPP":[66],"acyclic":[68,95],"digraphs":[69,96],"which":[70],"runs":[71],"considerably":[72],"faster":[73],"than":[74],"previously":[76],"best":[77],"algorithm.":[78],"based":[82],"new":[85],"insight":[86],"revealing":[87],"that":[88],"linearizability":[90],"can":[97],"be":[98],"seen":[99],"as":[100],"local":[102],"property.":[103],"Our":[104],"approach":[105],"extends":[106],"more":[109],"general":[110],"higher-order":[111],"shortest":[112],"path":[113],"problem.":[114]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
