{"id":"https://openalex.org/W2999683518","doi":"https://doi.org/10.23919/ecc51009.2020.9143743","title":"A generalized Bellman-Ford Algorithm for Application in Symbolic Optimal Control","display_name":"A generalized Bellman-Ford Algorithm for Application in Symbolic Optimal Control","publication_year":2020,"publication_date":"2020-05-01","ids":{"openalex":"https://openalex.org/W2999683518","doi":"https://doi.org/10.23919/ecc51009.2020.9143743","mag":"2999683518"},"language":"en","primary_location":{"id":"doi:10.23919/ecc51009.2020.9143743","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc51009.2020.9143743","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2001.06231","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025708846","display_name":"Alexander Weber","orcid":"https://orcid.org/0000-0002-4708-7583"},"institutions":[{"id":"https://openalex.org/I174004417","display_name":"Munich University of Applied Sciences","ror":"https://ror.org/012k1v959","country_code":"DE","type":"education","lineage":["https://openalex.org/I174004417"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alexander Weber","raw_affiliation_strings":["Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany","[Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany]"],"affiliations":[{"raw_affiliation_string":"Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I174004417"]},{"raw_affiliation_string":"[Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany]","institution_ids":["https://openalex.org/I174004417"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102897198","display_name":"Marcus Kreuzer","orcid":"https://orcid.org/0009-0008-3644-7134"},"institutions":[{"id":"https://openalex.org/I174004417","display_name":"Munich University of Applied Sciences","ror":"https://ror.org/012k1v959","country_code":"DE","type":"education","lineage":["https://openalex.org/I174004417"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Marcus Kreuzer","raw_affiliation_strings":["Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany","[Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany]"],"affiliations":[{"raw_affiliation_string":"Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I174004417"]},{"raw_affiliation_string":"[Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany]","institution_ids":["https://openalex.org/I174004417"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068993444","display_name":"Alexander Knoll","orcid":"https://orcid.org/0000-0003-4348-1708"},"institutions":[{"id":"https://openalex.org/I174004417","display_name":"Munich University of Applied Sciences","ror":"https://ror.org/012k1v959","country_code":"DE","type":"education","lineage":["https://openalex.org/I174004417"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alexander Knoll","raw_affiliation_strings":["Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany","[Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany]"],"affiliations":[{"raw_affiliation_string":"Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I174004417"]},{"raw_affiliation_string":"[Dept. of Mechanical, Automotive and Aeronautical Eng., Munich University of Applied Sciences, M\u00fcnchen, Germany]","institution_ids":["https://openalex.org/I174004417"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025708846"],"corresponding_institution_ids":["https://openalex.org/I174004417"],"apc_list":null,"apc_paid":null,"fwci":0.1444,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49078587,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"2007","last_page":"2014"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9994999766349792,"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/T10142","display_name":"Formal Methods in Verification","score":0.9994999766349792,"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/computer-science","display_name":"Computer science","score":0.7669479846954346},{"id":"https://openalex.org/keywords/dijkstras-algorithm","display_name":"Dijkstra's algorithm","score":0.741688072681427},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6562764644622803},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5181487798690796},{"id":"https://openalex.org/keywords/symbolic-execution","display_name":"Symbolic execution","score":0.4764281213283539},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.433504581451416},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.42209142446517944},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4137776494026184},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3812796473503113},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.34970709681510925},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.24892732501029968},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.1832473874092102},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13373175263404846},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.13248878717422485},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1282869577407837},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.11990231275558472}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7669479846954346},{"id":"https://openalex.org/C173870130","wikidata":"https://www.wikidata.org/wiki/Q8548","display_name":"Dijkstra's algorithm","level":4,"score":0.741688072681427},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6562764644622803},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5181487798690796},{"id":"https://openalex.org/C2779639559","wikidata":"https://www.wikidata.org/wiki/Q7661178","display_name":"Symbolic execution","level":3,"score":0.4764281213283539},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.433504581451416},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.42209142446517944},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4137776494026184},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3812796473503113},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.34970709681510925},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.24892732501029968},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.1832473874092102},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13373175263404846},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.13248878717422485},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1282869577407837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.11990231275558472},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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":4,"locations":[{"id":"doi:10.23919/ecc51009.2020.9143743","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc51009.2020.9143743","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2001.06231","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.06231","pdf_url":"https://arxiv.org/pdf/2001.06231","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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:2999683518","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2001.06231.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.2001.06231","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2001.06231","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2001.06231","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.06231","pdf_url":"https://arxiv.org/pdf/2001.06231","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"funders":[{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320334763","display_name":"Leibniz-Gemeinschaft","ror":"https://ror.org/01n6r0e97"},{"id":"https://openalex.org/F4320336863","display_name":"Leibniz-Rechenzentrum","ror":"https://ror.org/05558nw16"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2999683518.pdf","grobid_xml":"https://content.openalex.org/works/W2999683518.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W273656381","https://openalex.org/W1489726963","https://openalex.org/W1641312805","https://openalex.org/W1838714828","https://openalex.org/W2033077742","https://openalex.org/W2041701185","https://openalex.org/W2049680316","https://openalex.org/W2057096988","https://openalex.org/W2061936891","https://openalex.org/W2084943433","https://openalex.org/W2107173440","https://openalex.org/W2122311520","https://openalex.org/W2144965436","https://openalex.org/W2152784531","https://openalex.org/W2169528473","https://openalex.org/W2227557434","https://openalex.org/W2337661843","https://openalex.org/W2487779201","https://openalex.org/W2502734103","https://openalex.org/W2504175021","https://openalex.org/W2566091043","https://openalex.org/W2569628409","https://openalex.org/W2753203001","https://openalex.org/W2756915303","https://openalex.org/W2893322488","https://openalex.org/W2936521087","https://openalex.org/W2962709723","https://openalex.org/W2963701132","https://openalex.org/W2964326012","https://openalex.org/W2972859423","https://openalex.org/W3100135013","https://openalex.org/W3103706207","https://openalex.org/W3104168345","https://openalex.org/W3138807513","https://openalex.org/W3141459484","https://openalex.org/W6610028881","https://openalex.org/W6792319920","https://openalex.org/W7067586168"],"related_works":["https://openalex.org/W3046880377","https://openalex.org/W1520896331","https://openalex.org/W2886999287","https://openalex.org/W2064736805","https://openalex.org/W2407590628","https://openalex.org/W1971990575","https://openalex.org/W2022209918","https://openalex.org/W2990102050","https://openalex.org/W2422398296","https://openalex.org/W2795235041","https://openalex.org/W78347512","https://openalex.org/W2767843823","https://openalex.org/W2142347236","https://openalex.org/W2034088377","https://openalex.org/W2033077742","https://openalex.org/W3208431875","https://openalex.org/W3134674643","https://openalex.org/W2163068814","https://openalex.org/W3185739099","https://openalex.org/W1978009283"],"abstract_inverted_index":{"Symbolic":[0],"controller":[1],"synthesis":[2,8,70],"is":[3,27,64,133],"a":[4,50,117],"fully-automated":[5],"and":[6,16,41,94],"correct-by-design":[7],"scheme":[9,36],"whose":[10],"limitations":[11],"are":[12],"its":[13],"immense":[14],"memory":[15,106],"runtime":[17],"requirements.":[18],"A":[19],"current":[20],"trend":[21],"to":[22,28,54,73],"compensate":[23],"for":[24,31,86,95,101,105],"this":[25,46,128],"downside":[26],"develop":[29],"techniques":[30],"parallel":[32,96],"execution":[33,97],"of":[34,67,112,119,141],"the":[35,58,68,74,99,110,138],"both":[37],"in":[38,42,57,135],"mathematical":[39],"foundation":[40],"software":[43],"implementation.":[44],"In":[45,126],"paper":[47],"we":[48],"present":[49],"generalized":[51],"Bellman-Ford":[52],"algorithm":[53,78,80],"be":[55],"used":[56,76],"so-called":[59],"symbolic":[60],"optimal":[61],"control,":[62],"which":[63,132],"an":[65],"extension":[66],"aforementioned":[69],"scheme.":[71],"Compared":[72],"widely":[75],"Dijkstra":[77],"our":[79,142],"has":[81],"two":[82],"advantages.":[83],"It":[84],"allows":[85],"cost":[87,114],"functions":[88],"taking":[89],"arbitrary":[90],"(e.g.":[91],"negative)":[92],"values":[93,115],"with":[98,122],"ability":[100],"trading":[102],"processing":[103],"speed":[104],"consumption.":[107],"We":[108],"motivate":[109],"usefulness":[111],"negative":[113],"on":[116],"scenario":[118],"aerial":[120,124],"firefighting":[121],"unmanned":[123],"vehicles.":[125],"addition,":[127],"four-dimensional":[129],"numerical":[130],"example,":[131],"rich":[134],"detail,":[136],"demonstrates":[137],"great":[139],"performance":[140],"algorithm.":[143]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}